A  TEXT- BOOK  OF  LOGIC 


A  TEXT- BOOK  OF 
LOGIC ' 


BY 

ARTHUR  ERNEST  DA  VIES 

PKOFEMOX  or  PHILOSOPHY  IN  THE  OHIO  STATE  UNIVERSITY 


R.  G.  ADAMS  AND  COMPANY 
1915 


COPYRIGHT.  1915 

BY 
ARTHUR  ERNEST  DAVIES 


TO 
MY  FATHER 


339514 


PREFACE 

The  time  has  not  arrived  when  it  is  possible  or 
desirable  to  write  a  text-book  of  logic  for  elementary 
students  which  departs  very  considerably  from  the 
course  that  has  been  defined  by  university  require- 
ments in  various  parts  of  the  world.  Both  in  Eu- 
rope and  in  America  instruction  in  this  subject  has 
to  a  large  extent  been  controlled  by  what  may  be 
called  the  classical  tradition  of  which  Aristotle  and 
Mill  are  the  two  fountain  heads.  In  some  quarters 
this  fact  has  operated  as  a  hardship,  and  has  led 
to  open,  if  rather  one-sided,  criticism  of  the  subject's 
educational  usefulness,  on  the  one  hand,  and  has 
directed  attention  to  and  aroused  interest  in  the 
real  and  supposed  defects  of  the  traditional  logical 
doctrine,  on  the  other.  The  position  both  of  those 
who  maintain  the  conservative  attitude,  and  of  those 
who  would  substitute  for  the  old  some  new  kind  of 
logic,  is  capable  of  defence  up  to  a  certain  point, 
and  there  is  no  doubt  that  the  stirring  of  the  aca- 
demic waters  on  this  subject  will  result  at  some 
time  in  a  larger  freedom  in  the  choice  of  the  mate- 
rial and  methods  of  logical  instruction,  and  to  that 
extent  will  reduce  the  possibility  of  attributing  to 
the  subject  the  imperfections  of  temper  and  under- 
standing of  those  who  teach  it. 

I  hold  no  brief  for  traditionalism  in  logic,  and 
while  I  sympathise  with  and,  according  to  my 

vii 


Vlii  PREFACE 

ability,  appreciate  the  value  of  much  that  the  advo- 
cates of  the  newer  logics  have  contributed  to  our 
knowledge  of  the  methods  by  which  the  human 
mind  reaches  truth,  I  have  never  been  able  to  dis- 
possess myself  of  the  belief  that  the  older  logic 
in  some  measure  had  enabled  me  to  understand  what 
the  newer  logic  had  to  say.  Were  I  an  artist,  it 
would  be  my  desire  to  paint  the  ocean,  just  because, 
I  imagine,  it  is  so  constantly  changing  and  withal 
so  eternally  the  sama  A  similar  interest  may 
stimulate  one  to  observe,  in  all  the  ways  that  modern 
logic  is  making  familiar  to  us,  the  wonderful  change- 
fulness  and  practical  resourcefulness  of  the  mind's 
approach  to  truth ;  but  if  one  were  to  identify  logic 
with  the  observation  and  description  of  these  shift- 
ing phenomena,  he  would  be  in  the  position  of  the 
man  for  whom  the  ocean  was  no  more  than  the 
waves  that  rose  and  fell  and  broke  upon  its  bosom. 
The  human  mind  has  a  determinate  structure,  and 
it  is  with  that  structure,  so  far  as  it  is  displayed  in 
the  field  of  knowledge,  that  logic  aims  to  make  us 
acquainted.  And  I  do  not  believe  that  it  has  been 
reserved  for  our  own  times  to  utter  the  only  true 
words  on  this  subject,  nor  that  we  can  afford  to  neg- 
lect the  teaching  of  the  ancients.  Aristotle  defined 
logic  and  formulated  many  of  its  methods  in  a  way 
that  has  given  life  to  the  subject  for  over  two  thou- 
sand years,  and  much  that  is  modern  takes  its  point 
of  departure,  either  by  way  of  criticism  or  refining, 
from  what  he  wrote  in  the  beginning  of  the  science's 
existence.  It  is  not  to  be  understood,  of  course, 


PREFACE  IX 

that  the  traditional  doctrine  stands  in  no  need  of 
critical  examination.  The  reverse  is  the  fact.  The 
enormous  increase  of  knowledge  in  the  modern  era 
makes  it  necessary.  But  how  are  criticism  and 
revision  possible  if  the  subject  is,  as  some  seem  to 
think,  wholly  illusory,  or  if  we  remain  in  absolute 
ignorance  of  the  doctrine  upon  which  criticism  and 
revision  are  to  be  directed? 

It  seems,  therefore,  that  for  some  time  to  come 
logic  will  continue,  in  the  main,  to  be  traditional, 
and  that  books  of  logic  will  have  to  conform  to  the 
requirements  that  are  determined  by  that  fact. 
But  there  are  all  sorts  and  degrees  of  conformity, 
and  I  confess  to  a  liking  for  that  kind  and  degree 
which  is  not  inconsistent  with  the  exercise  of  the 
largest  liberty  of  one's  academic  conscience.  It 
would  not  be  surprising,  consequently,  if  it  were 
discovered  that  I  had  allowed  the  present  situation 
in  logic  to  sit  lightly  upon  me,  and  that,  where  it 
seemed  desirable,  I  had  departed  in  method  and  doc- 
trine from  traditional  views.  It  is  I  believe  in  some 
such  way  as  this,  rather  than  in  assuming  a  critical, 
not  to  say  captious,  attitude  toward  the  whole  of 
traditional  logic  that  the  best  interests  both  of  the 
subject  and  of  those  who  study  it  can  be  advanced. 

It  is  hardly  necessary  to  say  that  the  present 
book  as  a  whole  is  the  product  of  experience  in 
teaching  logic  to  elementary  and  advanced  students 
of  the  subject,  No  one,  I  am  convinced,  should 
attempt  to  write  a  text-book  in  any  subject,  and 
certainly  not  in  logic,  who  has  not  learned  in  the 


X  PREFACE 

practical  way  of  teaching  it  where  its  main  difficul- 
ties are  found,  and  who  has  not  had  an  oppor- 
tunity afforded  him  of  devising  methods  of  overcom- 
ing them.  For,  in  the  first  place,  a  text-book  must  be 
written  for  the  student,  that  is,  for  one  who  is 
presumed  not  to  know  anything  about  the  subject 
of  which  it  treats  and,  for  him,  the  greatest  service 
that  it  can  render  is  to  stimulate  an  interest  in  the 
problems  with  which  it  deals.  But  also  it  should 
be  an  instrument  in  the  hands  of  the  teacher  which 
facilitates  the  task  of  teaching,  and  adapts  itself 
to  the  purposes  that  he  may  hold  before  himself 
and  the  class.  However  far  my  book  may  be  from 
completely  fulfilling  these  objects,  I  hope  it  has 
entirely  escaped  the  capital  offence  of  substituting 
itself,  in  the  regard  and  thought  of  the  student,  for 
the  teacher,  and  that  it  can  not  be  accused  of 
helping  to  degrade  the  teaching  function  to  the 
mere  level  of  hearing  a  recitation.  I  trust,  there- 
fore, that  there  are  many  sections  that  will  be 
found  to  require  the  generative  touch  of  the  teacher, 
and  that  what  in  his  hours  of  preparation  may 
appear  to  the  student  as  a  valley  of  dry  bones  will 
be  vitalized  by  the  teacher  into  living  forms  in  the 
hours  spent  in  the  lecture  room. 

I  have  given  to  the  judgment  a  prominence  in 
the  order  of  topics  which  I  think  is  required  for  a 
true  comprehension  of  the  problem  of  logic,  and 
have  distinguished  between  it  and  the  proposition 
for  the  purpose  of  indicating  the  class  of  questions 
which  any  attempt  to  express  our  judgments  in 


PREFACE  XI 

words  quite  naturally  suggests.  If  I  am  not  mis- 
taken, current  controversy  in  philosophy  would 
sometimes  have  been  simplified,  if  indeed  the  occa- 
sion for  it  were  not  entirely  removed,  if  it  had  been 
distinctly  recognised  that  the  judgment  is  not  the 
proposition,  and  that  the  problems  of  each  are  quite 
distinct.  A  close  relationship  must,  of  course,  be 
recognised  between  judgments  and  propositions,  but 
I  am  not  without  hope  that  the  separate  treatment 
of  these  topics  will  meet  with  the  approval  of  my 
colleagues,  although  it  results  in  placing  at  the 
very  beginning  what  must  be  regarded  as  one  of  the 
difficult  chapters  of  the  book.  I  do  not  believe  that 
the  judgment  chapter  is  insuperably  difficult;  it  is 
not  more  difficult,  for  example,  than  is  the  neuro- 
logical material  to  which  the  psychologist  introduces 
his  students  at  the  very  outset  of  their  studies.  And 
I  may  say  that  the  effort  has  been  made  to  present 
the  subject  in  a  manner  as  simple  as  is  consistent 
with  the  real  complexity  and  difficulty  of  the  prob- 
lem. With  a  simplification  which  falsifies  a  topic  in 
the  interests  of  easing  the  task  of  student  or  teacher 
I  have  as  little  sympathy  as  I  have  with  the  reverse 
method  of  creating  or  magnifying  difficulties  for  the 
good  of  the  learner's  academic  soul.  But  we  must 
cultivate  in  ourselves  and  in  those  we  teach  the 
ability  to  recognise  a  difficulty  when  and  where  it 
exists,  and  to  face  it  with  determination,  and  this 
requires  from  teacher  or  pupil  neither  apology  nor 
praise. 


Xli  PREFACE 

With  respect  to  other  features  of  the  book,  I 
may,  perhaps,  be  expected  to  say  something  in  justi- 
fication of  the  relatively  detailed  account  that  has 
been  given  of  the  fallacies.  There  is,  in  fact,  little 
to  say,  and  that  little  I  trust  will  appear  quite  super- 
fluous to  any  one  who  has  read  the  chapters  in 
question.  Both  the  mode  of  treatment  and  the 
amount  of  space  given  to  the  subject  have  been 
determined  by  the  belief  that  the  problem  of  falla- 
cies has  not  received  as  a  rule  the  recognition  that 
it  deserves,  and  that  it  has  not  been  correlated  to 
the  main  logical  doctrines  in  a  sufficiently  organic 
way.  I  do  not  wish  to  be  understood  to  mean  that 
the  chapters  given  here  are  at  all  adequate  in  these 
respects  to  the  importance  I  conceive  the  subject 
to  have.  I  have,  however,  sought  to  avoid  leaving  the 
impression  that  the  subject  has  no  practical  or  pos- 
itive significance,  and  have  endeavoured  to  keep  the 
whole  discussion  in  close  relation  to  the  body  of 
logical  doctrine  developed  in  the  preceding  chapters. 
To  leave  the  student  with  some  degree  of  respect 
for  the  topic  as  a  whole  seems  to  me  to  be  decidedly 
worth  attempting,  especially  when  the  student  is 
one  who  is  making  acquaintance  with  the  subject 
for  the  first  time.  It  will  also  be  found,  I  think, 
that  the  two  chapters  in  which  the  fallacies  are  dis- 
cussed lend  themselves  readily  to  the  purposes  of  a 
review  of  the  main  logical  problems,  and  that  the 
new  point  of  view  from  which  these  problems  are 
considered,  the  point  of  view,  namely,  of  the  sources 
of  error  that  lurk  in  the  processes  of  logical  thinking, 


PREFACE  Xlll 

will  not  only  relieve  the  review  from  the  banalities 
that  usually  attach  to  a  twice  performed  task,  but 
may  be  found  to  make  the  problems  themselves  more 
articulate  and  significant.  At  any  rate,  if  we  begin 
our  logical  studies  with  the  object  of  finding  out 
what  is  meant  by  truth,  and  what  are  some  of  the 
forms  in  which  truth  exists,  one  would  think  that 
a  discussion  of  error  or  at  least  an  examination  of 
some  of  the  forms  in  which  error  exists,  would 
serve  to  emphasise  the  importance  and  the  character 
of  logical  problems.  And,  I  confess,  it  seems  to  me 
that  no  amount  of  technical  skill  in  the  manipulation 
of  technical  formulae  can  compensate  for  any  failure 
to  perceive  that  the  problems  of  logic  originate  in 
the  effort  to  think  and  to  express  ourselves  clearly 
and  correctly,  and  that,  therefore,  the  science  that  is 
devoted  to  the  study  of  the  principles  of  clear  and 
correct  thinking  is  one  in  which  any  person  that  has 
any  pretense  to  education  should  have  an  interest. 
And  in  this  connection  I  may  add  that  the  questions 
on  the  text  appended  to  each  chapter  are  designed 
as  much  to  stimulate  such  an  interest  as  to  test  a 
student's  acquaintance  with  the  details  of  the  dis- 
cussion; and  if  any  apology  for  printing  them  or 
for  making  them  so  numerous  is  needed,  I  can  only 
reply  that  my  own  students  say  that  they  have 
found  them  useful. 

I  confess  to  a  certain  compunction  in  offering 
to  the  public  a  book  on  logic  which  fails  to  discuss 
in  a  systematic  way  the  so-called  laws  of  thought, 
although  I  have  never  felt  the  necessity  of  apolo- 


Xiv  PREFACE 

gising  to  myself  for  failing  to  expound  to  my  ele- 
mentary students  so  recondite  a  subject.  I  really 
have  never  found  that  any  attempt  to  interest  be- 
ginners in  logic  in  this  problem  was  satisfactory 
either  from  my  own  or  from  their  point  of  view. 
The  book,  therefore,  does  in  this  particular  conform 
to  my  practice,  and  the  justification  that  may  be 
offered  is  that  it  is  pedagogically  and  scientifically 
preferable  for  the  student  to  discover  some  problems 
for  himself  in  the  course  of  his  studies  than  to  force 
them  in  a  more  or  less  artificial  manner  upon  his 
attention.  There  are  places  in  the  text  where  the 
subject  here  in  question  is  quite  near  the  surface, 
and  if  it  happens  to  break  through,  the  wise  teacher 
will  surely  not  fail  to  take  advantage  of  his  oppor- 
tunity. 

With  respect  to  the  general  outcome  of  such  a 
course  in  logic  as  is  outlined  in  this  book,  it  is 
enough  to  say  that  I  should  be  exceedingly  disap- 
pointed if  the  way  had  not  been  prepared  for  an 
intelligent  study  of  the  larger  treatises  on  the  sub- 
ject, and  if  the  door  had  not  been  opened,  though 
only  a  little  way,  through  which  the  student  might 
pass  to  a  study  of  the  perennial  problems  of  phil- 
osophy itself.  About  the  former  point,  it  is  only 
necessary  to  say  that  the  lists  of  advanced  refer- 
ences at  the  end  of  the  chapters,  limited  as  they 
necessarily  had  to  be,  are  intended  to  invite  indi- 
vidual students  and  whole  classes  to  read  more 
widely  and  on  a  more  elevated  plane  discussions  of 
the  problems  which  are  considered  in  the  text,  and 


PREFACE  XV 

to  which  reference  is  also  made  in  the  first  lists  of 
books.  An  experiment  on  the  possibility  of  profit- 
ably using  books  of  an  advanced  character  might 
be  made  by  the  student  himself  in  connection  with 
those  parts  of  the  text  which  fail  to  interest  or 
profit  him.  I  shall  not  be  surprised  if  very  often 
the  presumably  .more  difficult  reference  turns  out 
in  the  end  to  be  the  simpler  statement.  If  any 
one  should  doubt  the  value  of  logic  as  an  introduc- 
tory approach  to  the  problems  of  philosophy,  which 
is  the  second  point  mentioned  above,  I  can  only  say 
that  so  long  as  those  problems  continue  to  depend, 
to  the  extent  that  they  actually  do,  upon  logical 
construction,  there  is  absolutely  no  possibility  01 
understanding  what  the  problems  are,  much  less  of 
contributing  to  their  solution,  if  one  has  not  ac- 
quired a  mastery  of  the  instruments  of  logical  think- 
ing. But  not  only  is  this  true  in  respect  of  philos- 
ophy narrowly  interpreted;  an  acquaintance  with 
logical  methods  is  also  important  if  we  who  are  not 
philosophers  in  the  techincal  sense  of  the  word  are 
to  take  an  intelligent  attitude  toward  our  own  lives. 
Toward  such  an  end,  I  hope  some  contribution  has 
been  made  by  the  mode  in  which  the  logical  problem 
has  been  conceived,  and  by  the  manner  in  which  it 
has  been  worked  out. 

For  those  who  are  acquainted  with  the  liter- 
ature of  the  subject,  it  is  not  necessary  for  me  to 
name  the  sources  of  my  chief  indebtedness,  and  for 
those  who  are  not,  such  a  proceeding  would  savour 
of  a  vain  parade.  I  shall,  therefore,  content  myself 


XVI  PREFACE 

with  the  statement  that  I  have  learned  from  the 
masters  of  many  schools,  and  have  retained  a  grate- 
ful affection  for  them  all.  As  I  am  not  conscious  of 
being  a  partisan,  I  presume  that  even  those  who 
have  taught  me  most  would  hardly  recognise  me  as 
one  of  their  disciples.  The  public,  consequently,  will 
be  in  no  doubt  when  it  comes  to  /apportioning  praise 
or  blame  for  what  is  here  set  down,  although  it  is 
evident,  so  that  he  who  runs  may  read,  that  it  is 
not  all  made  up  out  of  my  own  head.  I  have  quoted 
when  necessary,  I  have  also  paraphrased,  I  have 
refused  neither  suggestion  nor  illustration  when  any 
of  these  methods  furthered  the  object  I  have  can- 
stantly  held  before  me  in  writing  these  pages.  I 
want,  therefore,  to  thank  all  who  by  their  published 
writings  have  rendered  themselves  liable  to  this 
sort  of -literary  piratage.  I  am  also  indebted  to  col- 
leagues for  particular  services  which  it  is  a  pleasure 
to  acknowledge.  Professor  Rudolph  Pintner  has 
read  many  of  the  chapters  in  the  first  half  of  the 
book,  and  made  suggestions  which  have  improved 
the  form  over  that  in  which  they  were  originally 
cast.  Mr.  A.  P.  Weiss  made  the  drawings  for  all 
the  figures,  and  also  read  some  of  the  sections  on 
induction.  Professor  David  R.  Major  has  read  all 
the  chapters  in  manuscript  and  in  proof.  I  feel  that 
his  criticisms  and  suggestions  have  been  invaluable. 
It  is  certainly  not  for  the  want  of  friendly  and 
intelligent  advice  that  I  may  sometimes  have  erred 
in  aim  and  execution.  The  final  stages  of  the  proofs 


PREFACE  XVll 

have  been  entirely  in  Dr.  Major's  hands.  I  take 
this  opportunity  to  acknowledge  assistance  that  has 
been  generously  rendered. 

Eltham,  Kent.  A.  E.  D. 

Feb.  25, 1915. 


CONTENTS 
CHAPTER  I. 

THE   PROBLEM   OF  LOGIC.  pAG£ 

The  Starting  Point 1 

Each  Science  has  a  Different  Subject-Matter 1 

The  Thought  Element  in  Knowldge 2 

What  we  Mean  by  Knowledge 5 

Knowledge  is  Systematic 6 

Logic  and  the  Knowledges 9 

The  Subject-Matter  of  Logic. 10 

Logic  as  Scientia  Scientiarum 11 

The  Humanistic  Influence  in  Logic 12 

Relation  of  Logic  to  Psychology 14 

Logic  as  an  Art 16 

What  Logic  is 18 

References  22 

Questions   22 

Exercises   23 

CHAPTER  II. 

THE   JUDGMENT. 

The  Meaning  of  Thought 24 

Judgment  and  Thought 28 

Other  Mental  Attitudes  Akin  to  Judgment 31 

Judgment  and  Groundless  Statements 33 

Practical  and  Theoretical  Aspects  of  Thought 35 

Relevant  Assertion   36 

The  Interest  Factor  in  Knowledge 44 

The  Object  of  Judgment 47 

The  Universe  of  Discourse 50 

xix 


XX  CONTENTS 

PAGE 

Truth,  Probability  and  Error 58 

References   70 

Questions   70 

Exercises   74 

CHAPTER  III. 

THE   PROPOSITION. 

Judgment  and  the  Proposition 76 

The  Import  of  Propositions 79 

Formal  Analysis  of  Propositions 84 

Terms   85 

Names  and  Words 88 

The  Copula   91 

The  Relational  View 92 

The  Existential  View 95 

Kinds  of  Propositions 98 

Relations  of  the  Main  Types  of  Propositions 99 

References  104 

Questions   104 

Exercises   105 

CHAPTER  IV. 

TERMS. 

Proposition   and  Terms 107 

Connotative  and  Denotative  Use  of  Terms 107 

Relation    of   the    Connotative    and    Denotative    Use    of 

Terms  110 

Distribution  of  Terms 114 

Some  Other  Characteristics  of  Terms ,- 117 

Concrete  Meaning   118 

Individual   Meaning:    Proper   Names   and   Designa- 
tions      120 

General  Meaning  124 

Collective  Meaning:  Individual  and  General 126 


CONTENTS  XXI 

PAGE 

Abstract  Meaning   130 

References  136 

Questions 136 

Exercises    138 

CHAPTER  V. 
TERMS  (Continued). 

The  Purpose  of  the  Chapter 139 

The  Basis  of  the  Distinctions  to  be  Studied 139 

Absolute  and  Relative  Meaning 140 

Positive  and  Negative  Meaning 143 

The  Conditions  of  Negative  Meaning 145 

The  Logic  of  Negation 149 

Privative  Meaning 153 

Disparate  and  Contrary  Meaning 155 

References  155 

Questions   156 

Exercises   157 

CHAPTER  VI. 

DEFINITION   AND   THE  PREDICABLES. 

The  Questions  of  this  Chapter 158 

Non-Ambiguity    160 

Ambiguity   162 

Translation    165 

When  Translation  may  be  Employed 166 

When  Definition  is  Required 167 

The  Method  of  Definition 168 

Definition  per  genus  et  differentiam 170 

Verbal  and  Real  Definition 173 

The  Relation  of  Purpose  to  Definition 175 

Tests  of  a  Definition 176 

The  Problem  and  Classification  of  the  Predicables 181 

The  Commensurable  Predicables..                                       .  183 


xxii  CONTENTS 

PAGE 

The  Non-Commensurable  Predicables 185 

References 186 

Questions   187 

Exercises 189 

CHAPTER  VII. 

DIVISION   AND   CLASSIFICATION. 

Relation  of  Definition  and  Division 190 

What  is  Meant  by  Logical  Division 191 

Other  Kinds  of  Division 193 

Fundamentum    Divisionis    195 

Questions  of  Terminology 199 

Rules  of  Logical  Division 200 

Dichotomy    205 

The  Tree  of  Porphyry 210 

Clasification  Defined  211 

Classification  and  Definition 212 

Classification  and  Division 213 

Kinds  of  Classification 215 

References  218 

Questions   219 

Exercises   220 

CHAPTER  VIII. 

CATEGORICAL  PROPOSITIONS. 

Types  of  Propositions 222 

Classification  of  Categorical  Propositions 223 

Quantity  of  Propositions 225 

The  Singular  Proposition 228 

The  Universal  Proposition 229 

Kinds  of  Universal  Proposition 230 

The  Particular  Proposition 230 

The  Indesignate  Proposition 232 


CONTENTS  xxiii 

PAGE 

Quality  of  Propositions 234 

The  Affirmative  Proposition 235 

The  Negative  Proposition 236 

The  Relation  of  Affirmative   and   Negative   Propo- 
sitions     238 

Exceptive  and  Exclusive  Propositions 240 

Compound  Propositions    244 

Modality  of  Propositions 246 

The  Assertoric  Proposition 247 

The  Problematic   Proposition 248 

The  Apodeictic  Proposition 250 

References   251 

Questions 252 

Exercises 253 

CHAPTER  IX. 

IMPLICATIONS    OF    CATEGORICAL    PROPOSITIONS. 

Relation  of  Quantity  and  Quality  in  Categorical  Propo- 
sitions       255 

Structural  Formulae  Indicating  the  Quantity  and  Qual- 
ity of  Propositions 256 

Distribution  of  the  Terms  of  the  Four  Categorical  Propo- 
sitions     259 

Meaning  and  Classes  of  Implication 263 

The  Opposition  of  Propositions 265 

Contrariety 266 

Subalternation    269 

Contradiction 272 

Subcontrariety    273 

The  Square  of  Opposition 275 

Nature  and  Methods  of  Eduction  278 

Obversion   279 

Conversion  283 

Contraposition 288 

Inversion    .  .   290 


xxiv  CONTENTS 

PAGE 

Summary  of  Eductions 291 

References  293 

Questions 293 

Exercises    296 

CHAPTER  X. 

CATEGORICAL   ARGUMENTS. 

The  Problem  of  the  Chapter 297 

Two  Preliminary  Questions 298 

Nature  of  the  Syllogism 301 

Structural  View  of  the  Syllogism 303 

Rules  of  the  Syllogism 305 

Figures  of  the  Syllogism 310 

Special  Rules  of  the  Four  Figures 312 

The  Moods  of  the  Syllogism 315 

The  Valid  Moods  of  the  Syllogism ' 316 

Relation  of  Moods  to  Figure 318 

References  322 

Questions   323 

Exercises   324 

CHAPTER  XI. 

OTHER  FORMS   OP   CATEGORICAL   ARGUMENT. 

Their  Relation  to  the  Syllogism 326 

Enthymeme 328 

Polysyllogism    329 

Types  of  Polysyllogism 331 

Sorites    332 

Epicheirema 335 

References  336 

Questions   337 

Exercises    .                                                                .  338 


CONTENTS  XXV 

CHAPTER  XII. 

DISJUNCTIVE  AND  HYPOTHETICAL  PROPOSITIONS  AND 

ARGUMENTS.  pAGE 

The  Disjunctive  Proposition 340 

The  Nature  and  Classes  of  Disjunctive  Syllogism 343 

The  Moods  of  the  Disjunctive  Syllogism 344 

The  Validity  of  Disjunctive  Arguments 345 

The  Hypothetical   Proposition 347 

The  Hypothetical  Syllogism 348 

The  Moods  of  the  Hypothetical  Syllogism 350 

Dilemmas 354 

Classes  of  Dilemma 357 

The  Validity  of  the  Dilemma 359 

References  361 

Questions   362 

Exercises   364 

CHAPTER  XIII. 

INDUCTION    AND    METHODS    PRELIMINARY    TO    INDUCTION. 

General  Statement  of  the  Problem 366 

What  is  Meant  by  Fact 367 

Nature  of  Reality 370 

Induction  by  Simple  Enumeration 372 

The  Value  of  Simple  Enumeration 375 

Empirical  Generalisation  376 

Colligation  of  Facts 378 

Parity  of  Reasoning 380 

References  381 

Questions   382 

Exercises    384 

CHAPTER  XIV. 

SOME  DESCRIPTIVE  METHODS  OF  INDUCTION. 

Relation  of  Numbers  of  Instances  to  an  Induction 385 

Logical  Significance  of  Statistical  Methods 389 

Qualitative  Methods  of  Observation 393 


XXVI  CONTENTS 

PAGE 

The  Nature  of  Scientific  Observation 395 

Experimental  Observation 400 

References   403 

Questions   404 

Exercises   405 

CHAPTER  XV. 

SOME    EXPLANATORY    METHODS    OF    INDUCTION. 

The  Nature  of  Scientific  Explanation 406 

The  Meaning  of  Analogy 409 

The  Logical  Character  of  Analogy 411 

The  Function  of  Analogy  in  Induction 416 

The  Nature  of  Hypothesis 419 

Objections  to  the  Use  of  Hypothesis 422 

Verification  of  Hypotheses 427 

Hypothesis  and  Theory 429 

References   431 

Questions   432 

Exercises    434 

CHAPTER  XVI. 

CAUSATION. 

General  Statement  of  the  Problem 435 

The  Practical  Aspect  of  the  Problem 436 

The  Theoretical  Aspect  of  the  Problem 438 

The  Genetic  Relation  of  the  Practical  and   Theoretical 

Views    440 

The  Origin  and  Nature  of  the  Causal  Problem 442 

The  Course  of  Our  Further  Discussion 444 

The  Time  Relations  of  Causal  Events 445 

The  Complex  Character  of  Causal  Events 449 

The  Necessity  of  Causal  Events 456 

The  Plurality  of  Causes 461 

References   4^7 

Questions   468 

Exercises    .                                                                 470 


CONTENTS  XXVii 

CHAPTER  XVII. 

MILL'S  EXPERIMENTAL   METHODS. 

Their  Historical  Position 471 

The  Nature  of  the  Problem  to  Which   These   Methods 

Apply   473 

Elimination  as  a  Method  of  Causal  Inquiry 474 

The  Method  of  Agreement 477 

The  Method  of  Difference 482 

The  Joint  Method  of  Agreement  and  Difference 486 

The  Method  of  Concomitant  Variations 492 

The  Method  of  Residues 496 

References  .« 501 

Questions   501 

Exercises    504 

CHAPTER  XVIII. 

FALLACIES. 

Fallacy  Defined    508 

Classification  of  Fallacies 511 

Fallacies  of  Interpretation 514 

Verbal  Ambiguity  515 

Equivocation   515 

Accent    517 

Composition    518 

Division    519 

Accident 520 

The  Converse  Fallacy  of  Accident 521 

Structural  Ambiguity 522 

Amphibole   522 

False  Parenthesis    524 

Fallacies  of  Implication 525 

Fallacies  of  Opposition 526 

Fallacies  of  Eduction . .  .529 


XXV111  CONTENTS 

PAGE 

Fallacies  of  Inference 531 

The  Deductive  Fallacies 533 

Categorical  Fallacies    533 

Fallacies  of  Four  Terms 534 

Fallacies   of  Insufficient   Premises 537 

Hypothetical  Fallacies   539 

Disjunctive   Fallacies    544 

References   548 

Questions    548 

Exercises    550 

CHAPTER  XIX. 
FALLACIES   (Continued). 

\ 

Inductive  Fallacies   552 

Fallacies  of  Language 553 

Fallacies  of  Observation 555 

Fallacies  of  Explanation 563 

Fallacies  of  the  Context 567 

Fallacies  of  Assumption 569 

Petitio  Principii 570 

Complex  Questions    572 

Ignoratio   Elenchi    573 

Non  Sequitur   576 

Fallacies  of  Interest 578 

References   584 

Questions    585 

Exercises  .  587 


CHAPTER  I 

THE   PROBLEM    OF  LOGIC 

The  Starting  Point.  It  is  customary  to  begin  the 
exposition  of  a  branch  of  knowledge  with  a  state- 
ment and  explanation  of  its  definition.  This  is  a 
useful  mode  of  procedure  when  it  can  be  presumed 
that  those  for  whom  one  writes  have  previously 
acquired  an  elementary  knowledge  of  the  subject  to 
which  the  definition  relates.  But  since  no  such  pre- 
sumption is  made  in  regard  to  those  who  may  be 
expected  to  read  this  book,  we  shall  postpone  for 
the  present  the  task  of  formulating  a  definition  of 
logic.  Meanwhile,  we  shall  discuss  a  number  of 
topics,  all  of  which  throw  light  upon  some  feature 
of  the  problem  of  logic,  and  each  of  which  will  con- 
tain suggestions  as  to  the  nature  of  the  subject  to 
the  exposition  of  which  this  book  is  devoted.  And 
we  shall  find  it  convenient  to  begin  our  discussion  of 
these  topics  by  asking  what  is  the  subject-matter 
of  which  logic,  in  all  its  various  stages  and  branches, 
is  the  study. 

Each  Science  has  a  Different  Subject-Matter.  It 
will,  perhaps,  help  to  emphasize  the  importance  of 
this  inquiry  if  we  recall,  first,  that  a  science  presup- 
poses the  existence  of  a  special  kind  of  material, 
called  its  subject-matter;  and,  second,  that  each 
science  has  a  different  subject-matter.  For  example, 
in  geology  we  learn  about  the  structure  of  the  earth's 

(i) 


2  A   TEXT-BOOK   OF  LOGIC 

surface ;  in  physiology,  about  the  functions  of  living 
organisms.  Physics  is  a  study  of  bodies  in  motion ; 
and  geometry,  of  figures  in  space.  In  these,  and  in 
similar  cases,  the  subject-matter  of  the  science  is 
the  material  which  the  scientist  observes  and  de- 
scribes. 

The  Thought  Element  in  Knowledge.  If  we  con- 
sider further  how  the  several  sciences  are  con- 
stituted, it  soon  becomes  evident  that  the  mate- 
rial selected  for  study  is  only  one  condition  of 
the  existence  of  a  science.  The  scientist  must  also 
think  about  his  material  before  his  knowledge  con- 
cerning it  can  have  the  characteristics  of  scientific 
knowledge.  He  must,  for  one  thing,  arrange,  or,  as 
it  is  said,  classify,  the  material  that  he  has  collected. 
It  is  not,  however,  the  purpose  of  this  section  to 
describe  the  methods  that  the  scientist  employs  in 
studying  his  material.  At  present,  we  wish  to  call 
the  student's  attention  to  the  fact  that  the  attainment 
of  any  kind  of  knowledge  is  impossible  without  an 
active  exercise  of  the  thinking  processes,  and  to 
warn  him  that  the  passive  flow  of  images  and  ideas 
through  consciousness  must  not  be  mistaken  for 
thinking.  It  is  true  that  without  images  and  ideas 
there  can  be  no  thought;  but  thinking  consists  in 
comparing  objects  with  one  another,  in  differen- 
tiating the  like  from  the  unlike,  in  combining  them 
into  more  complex  wholes,  in  relating  in  many  and 
diverse  ways  these  wholes  to  each  other,  etc.  Think- 
ing, in  other  words,  is  a  specialised  sort  of  mental 
activity,  an  activity  that  taxes  to  the  utmost,  and 


THE   PROBLEM    OF   LOGIC  3 

frequently  brings  into  play,  all  the  abilties  with 
which  the  human  mind  is  endowed.  It  is  the  supreme 
task  to  which  the  many  have  been  called;  but 
if  we  regard  it  lightly,  or  presume  that  it  can  be 
accomplished  without  toil,  or  if  we  erect  our  own 
incapacity  or  indolence  into  a  reason  for  the  useless- 
ness  of  the  endeavor,  we  must  abandon  the  hope  of 
joining  the  company  of  the  few  who  are  chosen.  It 
is,  therefore,  with  good  reason  that  logic  directs 
attention  to  the  function  of  thought  in  human  knowl- 
edge, for  thinking  is  the  one  way,  the  only  royal 
road,  to  the  goal  of  an  educated  life.  To  think  about 
the  objects  of  one's  experience  is,  then,  necessary 
if  knowledge  is  to  exist;  but  thinking,  it  must  also 
be  borne  in  mind,  is  "not  a  passive  suffering  of  some- 
thing, but  a  doing  of  something  with"  these  objects. 
Or,  as  Wundt  has  expressed  it,  "jedes  denken  ein 
Wollen." 

Not  only,  then,  must  we  think  if  we  are  to  attain 
scientific  knowledge ;  we  must  also  think  in  order  to 
attain  knowledge  that,  in  the  strict  sense,  cannot  be 
described  as  scientific.  Illustrations  of  the  truth  of 
this  statement  may  be  found  in  history,  economics, 
jurisprudence,  as,  indeed,  it  may  be  in  all  those  other 
studies  which,  like  these,  are  interested  in  the  ways 
in  which  the  various  needs  of  men  are  met  in  a  social 
organisation.  It  would  seem,  then,  that  wherever 
we  have  knowledge,  whether  it  be  in  the  form  of  the 
natural  or  the  historical  sciences,  as  these  others 
may  be  called,  we  have  a  witness  to  the  ways  in 
which  the  demands  for  thought  have  been  met.  In 


4  A   TEXT-BOOK   OF  LOGIC 

brief,  unless  we  think  about  the  material  that  obser- 
vation brings,  knowledge  cannot  exist ;  and,  further, 
it  is  what  we  think  that  converts  this  material  into 
definite  species  of  knowledge. 

The  following  illustration  may  throw  additional 
light  upon  the  statements  of  this  section,  and  empha- 
sise the  importance  of  thought  for  all  forms  of 
human  knowledge.  We  all  know  what  a  picture  puz- 
zle is,  —  a  collection  of  odd-shaped  and  variously 
coloured  pieces  of  cardboard  which,  when  put  to- 
gether in  their  proper  relations,  form  a  complete 
and  consistent  whole.  All  of  us,  moreover,  have 
experienced  difficulty  in  putting  the  pieces  of  card- 
board together  so  that  the  hidden  pattern  or  picture 
is  made  evident.  If,  now,  we  study  a  case  like  this, 
we  may  observe  that  the  difficulty  we  had  in  bring- 
ing out  the  pattern  was  not  due  to  the  lack  of  any- 
thing in  our  material,  —  all  the  pieces,  we  shall  sup- 
pose, were  before  us,  and  were  capable  of  being 
fitted  to  one  another  in  an  appropriate  way.  But 
the  task  of  putting  them  together  in  the  proper  way 
was  by  no  means  easy.  Where  was  the  source  of  our 
difficulty  ?  We  cannot  attribute  it  to  our  material ; 
and  most  of  us  would  agree  that  it  was  due  to  our 
inability  to  see  which  parts  should  come  next  and 
next  and  next.  If  anyone  chanced  to  observe  us  at 
our  task,  he  probably  would  have  heard  us  exclaim, 
'How  stupid  I  am!'  'What's  the  matter  with  me!' 
'Why  can't  I  see  it!'  That  is  to  say,  he  would  have 
heard  us  blaming  ourselves,  and  finding  fault  with 
the  things  we  were  doing  to  the  material  with  which 


THE   PROBLEM   OF  LOGIC  5 

we  were  working.  What  bearing,  one  may  ask,  does 
this  have  upon  the  question  before  us?  Just  this, 
that  if  we  are  to  solve  the  simplest  problem,  thought 
must  be  brought  to  bear  upon  the  material  which 
constitutes  the  subject-matter  of  that  problem. 
When  we  do  not  succeed  in  doing  this,  and  when, 
for  any  reason,  we  are  baffled  in  our  endeavour  to 
make  out  the  nature  and  relations  of  the  material 
we  are  studying,  a  special  emphasis  is  thrown  upon 
the  thought  factor,  the  one  which,  under  more  favor- 
able conditions,  is  liable  to  be  lost  sight  of  entirely. 
In  this  we  are  like  children  who  look  about  their 
world  delightfully  oblivious  of  the  fact  that  the  eyes 
provide  them  with  the  light  of  all  their  seeing.  It  is 
only  when  the  eyes  fail  that  one  becomes  conscious 
of  their  existence.  Similarly,  when  knowledge  fails 
an  unsuspected  factor  of  knowledge  gains  promi- 
nence, and  to  this  factor,  to  which  attention  is  thus 
drawn,  we  give  the  name  —  thought. 

What  we  mean  by  Knowledge.  The  student  who 
has  read  carefully  the  foregoing  paragraphs  will 
understand  what  we  mean  when  we  say,  —  we  are 
always  thinking  about  something.  The  italicised 
words  call  attention  to  the  two  factors  in  knowledge. 
There  is  the  object,  —  the  million-starred  heavens, 
or  the  one  solitary  maiden,  on  the  one  side :  and,  on 
the  other,  our  thoughts  about  this  object.  Both 
these  elements  —  object  and  thought  —  are  neces- 
sary to  knowledge.  Objects  that  no  one  thinks  about 
are  only  the  materials  of  knowledge,  and  thoughts 
that  are  not  thoughts  -  about  something  in  par- 


6  A  TEXT-BOOK   OF  LOGIC 

ticular  can  hardly  be  called  thoughts  at  all.  It  is 
only  when  our  thoughts  are  thoughts-about-objects 
that  we  give  them  the  name  of  knowledge.  This 
statement  holds  so  generally  that  by  knowledge  of 
any  sort  whatsoever  —  poetry  or  legend  or  history 
or  science  or  just  every-day  opinion  —  we  may  be 
understood  to  mean  our  thoughts-about-objects. 
Accordingly,  from  the  standpoint  of  our  analysis, 
knowledge=object-f  thought.  In  later  sections,  we 
shall  have  more  to  say  about  these  two  factors  of 
knowledge. 

Knowledge  is  Systematic.  If  we  consider  our 
thoughts-about  objects  with  some  care,  we  shall  ob- 
serve that  they  tend  constantly  to  become  fixed, 
orderly,  and  systematic.  This  is  not  an  accident ;  it 
is  rather  of  the  nature  of  a  demand  that  we  make 
upon  ourselves  and  our  fellows,  so  much  so  that  we 
dismiss  with  a  shrug  of  the  shoulders  the  thoughts 
of  any  one  who  fails  to  meet  it  with  a  fair  degree  of 
success.  We  may  say,  then,  that  we  are  all  alike  in 
having  ordered  thoughts ;  we  differ  only  with  respect 
to  the  degree  of  success  that  we  attain  in  intro- 
ducing that  particular  kind  of  order  that  makes  our 
thoughts  most  effective.  For  example,  there  is  a 
great  difference  in  the  coherence  of  the  thoughts  of 
an  insane  or  feeble-minded  person  and  those  of  the 
average  normal  person.  In  the  former  case,  we 
observe  both  a  frequent  change  of  the  subject  of  his 
thought,  and  an  obvious  looseness  of  connection  be- 
tween one  thought  and  another,  even  when  these 
refer  to  the  same  subject.  Sometimes  the  only  con- 


THE   PROBLEM    OF   LOGIC  7 

nection  that  can  be  observed  between  one  thought 
and  another  is  the  similarity  in  sound  of  the  words 
in  which  the  thoughts  are  expressed.  On  the  other 
hand,  we  expect  to  find  the  average  normal  person 
able  to  think  in  such  a  way  that  the  connection  be- 
tween one  thought  and  another  follows  the  line  of 
the  essential  connections  of  one  part  and  another  of 
the  subject  about  which  he  thinks.  When  this  is  the 
case,  we  call  the  person's  thinking  'systematic',  — 
systematic,  that  is,  in  the  sense  that  the  order  of  his 
thoughts  is  warranted  by  the  nature  of  the  subject 
to  which  his  thoughts  refer. 

Now  it  may  be  interesting  and  profitable  to  note 
what  are  the  conditions  of  systematic  thinking. 
There  are  three  that,  from  the  logical  standpoint, 
require  mention.  First,  there  is  the  difference, 
native  and  acquired,  in  the  ability  of  individuals  sys- 
tematically to  develop  by  thinking  any  subject  in 
which  they  may  be  interested.  We  recognise  the 
fact  that  one  person  is  more  highly  endowed  in  this 
respect  than  another  in  such  every-day  expressions 
as:  'He's  just  smart';  'All  there  is  to  say  is,  he's 
got  brains.'  But  we  also  recognise  the  fact  that  we 
are  all  capable  of  improvement,  however  excellent 
or  mediocre  our  native  endowment  may  be.  The 
great  national  organisations  for  the  education  of  the 
young  are  a  recognition  of  this  fact.  But,  of  course, 
all  that  we  can  hope  to  do  by  education  is  to  diminish 
the  difference  between  one  individual  and  another; 
we  do  not  expect  to  overcome  the  advantage  that 
lies  on  the  side  of  the  person  who  adds  to  a  high 


8  A  TEXT-BOOK   OF  LOGIC 

native  endowment  a  careful  and  industrious  train- 
ing. The  second  condition  of  systematic  thinking 
is  found  in  the  fact  that  not  all  the  subjects  about 
which  we  think  seem  capable  of  being  systematised 
with  the  same  degree  of  completeness.  For  example, 
we  do  not  find  in  the  social  sciences  the  same  degree 
of  coordination  that  we  find  in  the  natural  sciences ; 
and,  in  a  general  way,  we  may  attribute  this  to  the 
greater  complexity  of  the  subject-matter  of  the  for- 
mer as  compared  with  the  latter. 

It  may  be  observed,  thirdly,  that  not  every 
occasion  that  calls  for  thought  is  met  best  with  the 
strictest  and  most  thorough  exercise  of  our  thinking 
ability.  If  we  compare,  for  example,  the  thoughts 
of  the  man  of  business  with  those  of  the  economist, 
or  the  thoughts  of  the  politician  with  those  of  the 
political  scientist,  we  shall  see  that  they  differ,  not 
necessarily  in  proportion  to  the  abilities  of  the  indi- 
viduals to  think,  nor  directly  with  respect  to  the 
difficulties  of  the  subject-matter  about  which  they 
think ;  but  the  occasion  that  sets  the  thinker  his  par- 
ticular task  sets  also  the  limits  within  which  the 
task  is  to  be  carried  out.  The  same  thing  is  true  up 
and  down  the  line  of  our  every-day  observation  and 
experience.  The  man,  for  example,  who  carried 
over  into  social  life  the  passion  for  precision,  accu- 
racy, and  completeness  that  properly  belongs  to  a 
scientific  publication  would  be  voted  a  bore,  just  as 
surely  as  the  man  who  worked  in  his  laboratory  with 
the  leisurely  and  lax  methods  of  a  man  of  the  world 
would  be  pronounced  a  failure.  Circumstances  alter 


THE  PROBLEM  OF  LOGIC  9 

cases ;  and  logic  observes  that  in  any  of  the  depart- 
ments of  human  life  where  thought  is  called  for,  it 
is  only  the  degree  of  systematic  thinking  appro- 
priate to  the  circumstances  that  it  is  ever  necessary 
to  attain. 

Logic  and  the  Knowledges.  In  our  discussion  of 
what  knowledge  is  we  have  seen  that  knowledge  may 
exist  in  many  different  forms,  varieties,  depart- 
ments, or  branches.  For  example,  engineering,  psy- 
chology, bacteriology,  literature,  biology,  etc.,  are  so 
many  different  forms  of  the  one  tiling  we  call  knowl- 
edge. For  this  reason,  it  would  be  better,  simpler, 
and  more  concrete  if  we  were  to  accustom  ourselves 
to  speak  of  these  subjects  as  ^knowledges'  whenever 
we  wished  to  refer  to  the  plurality  of  the  depart- 
ments of  knowledge.  We  have  a  precedent  for  this 
usage  in  that  we  speak  more  often  of  the  sciences 
than  we  do  of  science.  By  knowledges,  therefore, 
we  mean  the  several  varieties,  forms,  or  kinds  into 
which  knowledge  has  been  observed  to  falL  Now 
we  may  observe  that,  historically,  most  of  the  other 
subjects  of  knowledge  existed  before  logic  was  for- 
mulated into  a  science.  Mathematics,  astronomy, 
physics,  zoology,  political  and  social  philosophy,  for 
example,  are  must  older  branches  of  knowledge  than 
logic.  And  if  to  this  we  add  the  fact  that  logic  came 
into  existence  as  a  result  of  a  study  of  the  methods 
of  these  sciences,  we  shall  see  that  it  was  the  exist- 
ence of  the  knowledges  that  made  logic  possible 
rather  than  the  existence  of  logic  that  made  them 
possible.  Hence,  it  would  seem  to  be  true  that  while 


10  A   TEXT-BOOK   OF  LOGIC 

every  form  of  knowledge  may  be  cultivated  and  may 
flourish  independently  of  logic,  logic  cannot  even 
begin  to  be  unless  some  of  the  forms  of  knowledge 
have  already  established  themselves. 

The  Subject-Matter  of  Logic.  What,  now,  we 
may  ask,  is  the  relation  of  logic  to  the  two  factors 
of  which  all  knowledge  is  comprised?  And,  first, 
what  is  its  relation  to  the  subject-matter  of  the  other 
sciences?  The  question  needs  only  to  be  asked  to 
be  answered ;  for  it  is  obvious,  in  the  light  of  what 
has  already  been  said,  that  no  two  departments  of 
knowledge  study  the  same  material.  Logic,  there- 
fore, cannot  study  the  same  subject-matter  as  any 
other  science  without  losing  its  identity  by  becoming 
absorbed  in  that  science.  For  example,  if  logic  were 
to  study  the  origin,  growth,  and  function  of  political 
institutions,  the  result  would  be,  not  a  new  knowl- 
edge, but  an  old  one  under  a  new  name.  Political 
science  and  logic  would  then  be  the  same  things.  In 
like  manner,  if  logic  were  the  study  of  plants  it 
would  be  identical  with  botany.  Further  illustra- 
tion is  not  necessary.  The  subject-matter  of  logic 
is  not  identical  with  that  of  any  one  of  the  other 
knowledges.  What,  secondly,  is  its  relation  to  the 
thought  factor  which,  as  we  have  seen,  is  present 
in  all  knowledge?  Our  answer  is  that  it  is  this 
thought  factor  in  the  various  knowledges  that  logic 
makes  the  direct  object  of  its  study.  But  logic's 
relation  to  this  thought  element  is  different  from 
that  of  any  of  the  other  sciences.  In  the  several 
knowledges,  thought  is  the  means  by  which  the 


THE   PROBLEM    OF   LOGIC  11 

qualities  and  relations  of  objects  are  described  and 
explained.  Ordinarily,  we  are  no  more  aware  of  its 
presence,  than  we  are  of  the  pane  of  glass  through 
which  we  look  out  upon  the  landscape  that  lies  out- 
side our  window.  But  if,  for  any  reason,  we  become 
curious  to  know  how  thought  does  its  work,  to  find 
out  whether  it  follows  any  method,  we  should  then 
set  thought  before  our  minds  as  a  distinct  object  of 
study,  and  the  resulting  knowledge  would  be  called 
logic.  That  is  to  say,  logic  arises  when  the  thought 
factor  which  is  present  in  all  knowledge  is  set  before 
the  mind  as  a  subject  of  investigation.  Thought 
then  becomes  the  material  of  a  special  study,  and  the 
name  of  that  study  is  logic. 

Logic  as  Scientia  Scientarium.  We  have  just  seen 
that  logic  is  the  science  that  is  interested  in  the  way 
in  which  thought  does  its  work  in  the  several  fields 
of  knowledge.  Now  we  have  previously  seen  that 
we  are  not  everywhere  equally  successful  in  system- 
atising  our  thoughts-about-things.  Some  branches 
of  knowledge  are  more  loosely,  and  some  are  more 
closely,  organised.  This  fact  we  may  attribute  in 
part  to  the  greater  complexity  of  the  subject-matter 
of  some  of  the  knowledges.  History,  for  example, 
is  a  less  exact  science  than  is  physics  just  in  propor- 
tion to  the  greater  complexity  of  the  material  that 
it  studies,  and  to  the  difficulty  of  bringing  its  mate- 
rial under  controlled  observation.  Now,  in  this  con- 
nection, the  question  arises  —  Do  the  several  depart- 
ments of  knowledge  equally  well  provide  guidance 
for  the  formulation  of  logical  doctrine?  If  some 


12  A  TEXT-BOOK   OF  LOGIC 

branches  of  knowledge  are  better  articulated  than 
others,  should  we  not  expect  that  the  former  would 
illustrate  the  methods  of  thinking  more  perfectly 
than  those  branches  that  have  not  taken  on  the  same 
degree  of  coordination;  and,  further,  if  we  can 
find  any  group  of  knowledges  that  stands  pre-emi- 
nent in  this  respect,  should  we  not  save  time  and 
trouble  by  making  it  the  basis  of  our  study  of  logical 
doctrine?  Such  questions  have  been  asked,  and  it 
has  been  customary  to  answer  them  in  the  affirm- 
ative. Thus  logicians,  from  the  days  of  Aristotle 
to  the  present  time,  have  expounded  the  subject  of 
logic  with  their  eyes  on  the  methods  adopted  by  the 
better  articulated  sciences ;  and,  by  some,  the  study 
of  logic  has  been  confined  to  an  examination  of  the 
methods  that  have  proved  useful  in  reaching  the 
truth  in  such  sciences.  From  this  point  of  view, 
logic  has  been  looked  upon  as  a  science  that  lies  hid- 
den in  the  various  sciences,  very  much  as  the  pattern 
lies  hidden  in  a  picture  puzzle.  All  that  needs  to  be 
done,  according  to  this  view,  is  to  bring  logic  into 
the  light  that  it  may  direct  the  labors  of  future 
workers  in  the  field  of  the  sciences.  It  is  in  this 
sense  that  logic  is  spoken  of  as  scientia  scientiarum : 
it  is  the  science  of  sciences  in  the  sense  that  it  under- 
lies and  gives  direction  to  all  the  work  that  science 
undertakes  to  do. 

The  Humanistic  Influence  in  Logic.  That  view  of 
logic  which  identifies  it  with  the  study  of  scientific 
method  has  always  been  considered  a  little  partial 
and  extreme,  and  it  is  doubtful  if  Aristotle,  who 


THE   PROBLEM   OF  LOGIC  13 

was  the  first  and  greatest  of  the  formulators  of 
logical  doctrine,  and  whose  authority  has  been  ap- 
pealed to  in  support  of  this  position,  would  subscribe 
to  it.  It  is  probable,  as  Minto  has  shown,  that  in 
organising  his  logic,  Aristotle  had  in  mind,  as  much 
the  formulation  of  the  rules  of  dispute  in  the  social 
life  and  court  procedure  of  his  times,  as  the 
systematisation  of  the  methods  of  thought  in  the 
body  of  the  scientific  knowledge  of  his  day.  How- 
ever that  may  be,  it  is  certain  that  our  own  times 
are  witnessing  a  marked  humanistic  reaction  against 
a  stiff  and  formal  view  of  logic,  and  modern  logi- 
cians are  looking  to  the  less  exact  forms  of  knowl- 
edge for  enlightenment  as  to  the  way  in  which  the 
business  of  thought  is  carried  on ;  indeed,  their  study 
now  extends  to  the  ways  in  which  difficulties  arise 
and  are  overcome  in  our  everyday  life.  This  exten- 
sion of  the  field  within  which  the  logician  pursues 
his  studies  cannot  be  taken  as  an  evidence  of  indif- 
ference to  a  strictly  logical  doctrine ;  rather  must  it 
be  viewed  in  the  light  of  what  is  taking  place  in  other 
departments  of  knowledge  where  an  investigation 
of  the  simpler,  more  primitive,  forms  has  been  found 
to  elucidate  much  that  was  obscure  in  the  more  com- 
plex forms  of  the  subject-matter  studied  by  these 
departments.  In  zoology,  for  example,  interest  in 
the  simpler  organisms  has  flooded  with  light  our 
understanding  of  the  more  complex  ones,  and  in  psy- 
chology the  study  of  the  mental  processes  of  young 
children  and  of  the  feeble  minded  has  added  to  our 
understanding  of  the  adult,  normal  mind.  Hence  it 


14  A   TEXT-BOOK    OF   LOGIC 

is  felt  that  if  we  consider  those  methods  of  thought 
which,  in  some  of  the  sciences  and  in  the  ordinary 
business  of  life,  have  not  taken  on  a  strictly  rigid 
form,  we  shall  be  able  to  understand  the  nature  of 
thinking  in  a  more  satisfactory  manner  than  if  we 
confined  our  observation  to  those  sciences  in  which 
the  highest  degree  of  precision  in  methods  had  been 
attained. 

Relation  of  Logic  to  Psychology.  We  have  used 
the  term  'thought'  in  the  foregoing  pages  in  a  some- 
what broad  way.  It  has  meant,  in  general,  the  men- 
tal factor  which  is  never  absent  from  the  knowledge 
experience.  Now  the  question  may  arise  whether  in 
claiming  thought,  in  this  sense,  as  the  special  sub- 
ject-matter of  logic  we  have  not  confused  logic  with 
psychology.  For  what  is  psychology  if  it  is  not  a 
study  of  mental  processes? 

Now  there  are  two  ways  in  which  we  may  dis- 
tinguish between  logic  and  psychology.  In  the  first 
place,  we  may  remark  that  there  is  a  quantitative 
difference  between  the  two.  Grant,  for  the  time 
being,  that  the  subject-matter  of  both  these  sciences 
falls  within  the  field  that  we  usually  designate  as 
mental,  it  may,  nevertheless,  be  said  that  not  all  that 
is  mental  is  included  in  the  scope  of  logical  inquiry. 
Logic  is  interested  mainly,  if  not  exclusively,  in 
what  are  called  the  cognitive  processes;  that  is,  in 
those  processes  in  and  through  which  we  either 
affirm  or  deny  something.  But  cognition  in  the 
strict  sense,  cannot  claim  to  be  more  than  a  very 
small  part  of  one's  mental  life.  The  latter,  and  so 


THE   PROBLEM   OF  LOGIC  15 

the  field  of  psychological  inquiry,  includes,  in  addi- 
tion to  knowledge  or  cognition,  other  kinds  of  men- 
tal processes,  e.  g.,  feelings,  emotions,  volitions.  The 
whole  field  of  the  conscious  life  lies  open  to  the  in- 
vestigation of  psychology;  but  logic  is  interested 
chiefly  in  that  part  of  it  that  is  called  cognition,  and 
in  the  other  parts  only  so  far  as  they  help  us  to 
understand  what  human  knowledge  is. 

In  the  second  place,  we  may  remark  that  although 
logic  and  psychology  both  study  the  cognitive  proc- 
esses, they  do  not  study  them  from  the  same  point 
of  view.  Psychology  is  satisfied  when  it  has  de- 
scribed and  explained  the  mental  changes  that  take 
place  in  a  cognitive  process.  Logic  is  concerned,  not 
with  the  natural  history  of  cognition,  but  with  cog- 
nition as  an  instrument  by  means  of  which  the  world 
of  reality — minds  and  things — is  understood.  That 
is,  the  images  and  ideas  which  make  up  any  cognitive 
process,  and  which  psychology  endeavours  merely  to 
describe  and  explain,  are,  from  another  point  of 
view,  taken  to  represent  objects  in  the  real  world; 
and  it  seems  to  be  the  function  of  these  images  and 
ideas  to  place  those  who  have  them  in  communica- 
tion or  contact  with  objects  which  exist  in  some  sort 
of  independence  of  these  images  and  ideas.  It  is  this 
character  of  images  and  ideas  as  affording  us  a 
knowledge  of  a  world  of  objects  that  is  the  stand- 
point of  logic,  and  which  enables  us  to  distinguish 
the  logical  from  the  psychological  method  of  dealing 
with  the  cognitive  processes.  Logic  is  not  interested 
to  know  what  images  and  ideas  are  present  in  con- 


16  A  TEXT-BOOK   OF  LOGIC 

sciousness,  but  whether  the  images  and  ideas  that 
we  entertain  are  true,  that  is,  afford  us  accurate 
knowledge  of  the  objects  which  they  represent  and 
to  which  they  point.  Or,  to  put  it  more  succinctly, 
logic  studies  the  conditions  of  the  truth  or  falsity 
of  our  ideas,  a  problem  which,  for  psychology,  is 
quite  indifferent  or  non-existent. 

Logic  as  an  Art.  It  is  sometimes  said  that  logic  is 
an  art  as  well  as  a  science.  The  meaning  of  this 
statement  can  be  made  clear,  if  we  bear  in  mind 
that  the  term  'art'  is  used  in  two  senses.  In  the 
first  and  most  common  meaning,  it  refers  to  the 
developed  skill  that  one  acquires  through  practice 
of  a  set  of  more  or  less  mechanised  movements.  If, 
for  example,  you  go  into  a  machine  shop  and  watch 
the  workmen  at  their  tasks,  you  will  find  them  en- 
gaged in  different  activities,  and  displaying  varying 
degrees  of  skill.  It  is  this  ability  to  do  a  given  task 
with  some  degree  of  proficiency  that  we  call  the 
workman's  art.  Art  is,  then,  a  specialised  ability 
to  do.  On  the  other  hand,  there  is  an  ability,  much 
more  specialised  than  the  mechanic's,  which  con- 
sists in  the  perception  of  how  a  task  should  be  done, 
but  which  does  not  necessarily  carry  with  it  an 
ability  to  perform  it.  The  engineer,  for  example, 
is  able  to  plan  and  superintend  building  enterprises, 
although  he  does  not  have  the  ability  of  the  work- 
men upon  whom  he  must  rely  if  these  enterprises 
are  to  be  translated  into  steel  and  brick  and  stone. 
The  skilled  workman  and  the  engineer  display  two 
different  orders  of  practical  ability,  and  we  may 


THE   PROBLEM   OF   LOGIC  17 

speak  of  each  one  of  them  as  possessing  and  prac- 
ticing an  art. 

Now,  when  logic  is  spoken  of  as  an  art,  it  is  well 
to  be  clear  whether  we  are  using  the  term  art  in  the 
first  or  in  the  second  of  the  two  meanings  just  dis- 
tinguished; whether  we  are  thinking  of  logic  as 
giving  to  its  students  the  ability  to  think  correctly, 
or  whether  we  are  thinking  of  it  as  giving  its  stu- 
dents the  ability  to  detect  the  correctness  and  incor- 
rectness of  arguments.  We  are  inclined  to  the 
opinion  that,  in  the  case  of  logic,  these  two  meanings 
cannot  be  separated,  and  that  in  learning  the  regu- 
lative principles  of  logic  we  are  at  the  same  time 
acquiring  the  ability  to  order  our  thoughts  in  a  log- 
ical manner.  The  reason  for  this  opinion,  briefly 
stated,  is  that  the  study  of  logic  is  and  must  remain 
unprofitable  to  anyone  who,  while  he  is  studying  it, 
does  not  practice  the  methods  of  logical  thinking. 
The  meaning  of  this  statement  will  become  clearer 
as  we  proceed,  but  it  should  be  taken  by  the  student 
as  a  suggestion  that  the  way  to  gain  a  knowledge  of 
this  subject  is  to  think  each  step  logically  as  it  is 
unfolded  in  the  successive  chapters.  For  example, 
we  shall  presently  be  speaking  about  terms,  and  we 
shall  call  such  things  as,  'the  Sultan  of  Turkey/ 
'good,'  'H2S04,'  'man/ — terms.  Now,  it  is  obviously 
impossible  for  anyone  to  memorise,  or  even  to  make, 
a  list  of  the  things  that  logic  calls  terms.  The  only 
alternative,  therefore,  is  for  the  student  to  acquire 
the  ability  to  think  —  term,  to  understand  what  a 

3 


18  A  TEXT-BOOK   OF  LOGIC 

term  is.  When  he  has  done  this,  he  will  have  to 
employ  this  acquired  ability  in  all  his  subsequent 
study,  so  that  it  never  becomes  rusty  through  dis- 
use. The  same  remark  applies  to  all  the  topics  of 
which  logic  treats.  In  this  sense,  therefore,  the 
study  of  logic  is  at  the  same  time  practice  in  the 
methods  of  logic;  and  it  is  because  we  cannot  ac- 
quire a  knowledge  of  the  correct  methods  of  thought 
without  at  each  step  practicing  these  methods  that 
logic  may  be  said  to  be  an  art  in  both  of  the  senses 
defined  in  the  beginning  of  this  section. 

What  Logic  is.  We  may  now,  with  a  summary 
of  the  foregoing  discussion  in  mind,  undertake  a 
statement  of  what  logic  is.  We  have  seen  (1)  that 
logic  presupposes  the  existence  of  knowledge  in  one 
or  more  of  its  several  forms,  and  that  it  has  sus- 
tained this  relation  to  the  other  knowledges  from 
the  very  beginning.  Aristotle,  as  we  said,  was 
prompted  to  write  his  treatises  on  logic  from  the 
desire  that,  along  with  the  improvement  in  the 
sciences  and  arts,  there  should  go  the  consciousness 
of  the  method  by  which,  in  these  fields,  conclusions 
were  being  reached.  Logic,  therefore,  was  not  an 
invention  of  new  instruments  of  research  and  knowl- 
edge, but  the  formulation  and  systematisation  of 
those  that  in  use  had  already  proved  their  effective- 
ness. Consequently,  we  said  (2)  that  when  logic 
sets  about  its  task,  it  distinguishes  between  the  sub- 
ject-matter and  the  thought  element  in  the  knowl- 
edges, and  erects  the  latter  into  a  separate  object 
of  study.  Logic,  therefore,  is  a  study  of  the  relation 


THE   PROBLEM   OF  LOGIC  19 

of  thought  to  human  knowledge.  But,  in  this  con- 
nection, we  had  to  point  out  (3)  that  the  interest  of 
logic  in  thought  is  different  from  that  which  the 
several  knowledges  have  in  it.  The  knowledges  aim 
to  reach  conclusions  that  increase  our  understanding 
of  the  nature  of  the  objects  they  select  for  study. 
It  is  true  that  this  increased  understanding  is 
reached  by  thinking;  but,  so  long  as  results  are 
reached,  the  scientist  is  no  more  concerned  with 
thought  than  is  a  farmer  with  the  engine  that  drives 
the  machine  that  threshes  his  grain.  This  is  not 
the  case  with  logic.  It  studies  thought  with  a  view 
to  finding  out  its  methods  of  work.  From  this  point 
of  view,  therefore,  we  may  say  that  logic  is  a  science 
of  the  methods  of  correct  thinking.  But  (4)  if  logic 
is  to  be  guided  by  the  best  examples,  it  will  naturally 
be  interested  in  the  methods  of  the  natural  sciences. 
The  influence  of  this  interest  of  logic  in  the  natural 
sciences  has  been  to  restrict  unduly  the  scope  of  log- 
ical inquiry,  and  thereby  to  give  to  logic  an  impor- 
tance that  originally  did  not  belong  to  it.  The 
restriction  is  seen  in  the  definition  of  logic  as  a  study 
of  scientific  method,  and  the  new  importance  it  thus 
assumes  is  expressed  in  its  claim  to  be  the  scientia 
scientiarum,  —  the  science  that  makes  all  the  other 
sciences  possible  and  real.  In  this  connection,  we 
pointed  out  (5)  that  this  view  could  not  claim  the 
support  of  the  earliest  writers  on  the  subject,  and 
that  in  our  own  times  a  positive  reaction  against  it 
has  set  in.  The  form  that  the  reaction  has  taken  is 
to  extend  the  field  of  logical  observation  so  as  to  in- 


20  A   TEXT-BOOK   OF  LOGIC 

elude  not  only  the  more  highly  specialised  sciences, 
such  as  physics  and  chemistry,  but  also  those  that 
are  less  fully  developed,  such  as  the  biological,  social, 
and  historical  sciences.  From  this  standpoint,  logic 
is  a  study  of  the  methods  of  human  knowledge  of 
whatever  kind  the  knowledge  may  happen  to  be.  In 
the  section  on  psychology  and  logic  we  saw  (6)  that 
thought  may  be  studied  in  two  quite  different  ways. 
We  may  study  thought,  for  example,  as  a  series  of 
consciousnesses  made  up  of  various  elements  and 
possessing  various  attributes.  This  is  psychology. 
If,  however,  we  study  the  function  of  thought  in 
affording  us  a  knowledge  of  the  real  world,  we  are 
led  to  a  very  different  result,  and  the  kind  of  knowl- 
edge thus  reached  will  be  logical  rather  than  psycho- 
logical in  character.  For  logic,  that  is  to  say, 
thought  has  a  meaning  over  and  above  what  thought 
is  as  an  item  in  a  stream  of  consciousness.  What 
thought  is  or  is  like  is  one  thing,  and  what  thought 
means  and  does  it  another.  It  is  from  the  latter 
point  of  view  that  logic  studies  it.  If,  therefore, 
meaning,  as  one  writer  says,  is  a  "product  of  thought 
in  its  relation  to  reality,  or  of  reality  in  relation  to 
thought,"  logic  may  be  defined  as  a  science  of  the 
development  of  meaning,  or,  more  briefly,  as  the 
science  of  meaning. 

Only  one  more  point  need  be  raised,  namely,  in 
what  sense  logic  is  a  science  at  all.  In  the  last  sec- 
tion we  saw  that  logic  is  an  art  in  the  sense  that 
engineering  is  an  art,  but  we  also  saw  that  as  such 


THE   PROBLEM   OF  LOGIC  21 

it  is  an  art  in  a  somewhat  special  sense.  It  is,  if 
we  may  say  so,  an  intellectual  art,  an  art  that  con- 
sists in  knowing  how  certain  things  should  be  done. 
In  this  respect,  logic,  to  use  Minto's  illustration  of 
the  Aristotelian  logic,  may  be  likened  to  "Cavendish 
on  Whist,"  —  a  book  that  states  the  rules  and  illus- 
trates the  methods  of  playing  the  game.  We  have 
done  ample  justice  to  this  feature  of  logic,  and  the 
student  is  not  likely  to  lose  sight  of  its  importance 
as  we  proceed.  But  we  now  ask  whether  it  is  also, 
in  any  sense,  a  science;  in  the  sense,  for  example, 
that  physics  and  chemistry  are  sciences.  Now  we 
ought  to  be  clear  that  these  sciences  do  not  exist  for 
the  purpose  of  providing  rules  that  students  may 
follow  in  performing  laboratory  experiments.  If 
this  were  the  whole  extent  of  the  scientific  character 
and  purpose  of  these  subjects,  they  would  differ  in 
no  respect  from  the  practical  sciences  in  which  we 
learn  how  certain  things  are  done.  If,  however,  we 
consider  these  sciences  more  carefully  we  shall  see 
that  they  ^aim  to  formulate  principles  or  laws,  and 
that  it  is  only  as  the  experiments  enable  us  to  ascer- 
tain these  principles  that  they  have  their  perfect 
work.  So  we  may  say  with  respect  to  logic.  It  has  its 
experimental  side,  and  it  formulates  rules  and  states 
the  methods  of  correct  thinking ;  but  it  goes  beyond 
this  and  tries  to  express  the  laws  or  the  principles 
to  which  every  concrete  case  of  thinking  actually 
conforms.  In  the  light  of  this  fact,  we  may  conve- 
niently bring  this  chapter  to  an  end  with  the  state- 


22  A  TEXT-BOOK   OF  LOGIC 

ment  that  logic  is  a  study  of  the  methods  of  correct 
thinking  and  of  the  principles  on  which  these  meth- 
ods are  based. 

REFERENCES 

B.  Bosanquet,  The  Essentials  of  Logic,  Ch.  I. 

J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Ch.  I. 
J.  G.  Hibben,  Logic,  Inductive  and  Deductive,  Introduction  I. 
S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  I. 
W.  Minto,  Logic,  Deductive  and  Inductive,  Introduction  I. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Ch.  I. 

ADVANCED 

J.  M.  Baldwin,  Thought  and  Things,  Vol.  I,  Ch.  I. 

W.  R.  B.  Gibson,  The  Problem  of  Logic,  Introduction. 

H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Ch.  I. 

H.  Lotze,  Logic,  Vol.  I.,  Introduction. 

F.  C.  S.  Schiller,  Formal  Logic,  Ch.  I. 

C.  Sigwart,  Logic,  Vol.  I,  Introduction. 

J.  Welton,  Manual  of  Logic,  Vol.  I.,  Ch.  I.,  II. 

QUESTIONS 

1.  How  do  the  various  sciences  differ  from  one  another? 
Illustrate. 

2.  What  function  has  thought  in  the  several  sciences,  and 
what  reason  can  you  give  for  your  answer? 

3.  What  do  you  understand  by  knowledge,  and  into  what 
two  factors  may  all  knowledge  be  analysed? 

4.  What  is  meant  by  calling  knowledge  systematic? 

5.  Upon  what  three  factors  does  the  systematisation   of 
knowledge  depend? 

6.  Is  all  knowledge  equally  systematic?    Illustrate. 

7.  What  is  meant  by  'knowledges'? 

8.  "It  is  the  knowledges  that  make  logic  possible."     Ex- 
plain. 


THE   PROBLEM   OF  LOGIC  23 

9.     What  is  the  subject-matter  of  logic?    What  is  the  rela- 
tion of  this  subject-matter  to  the  other  sciences? 

10.  What  is  meant  by  calling  logic  scientia  scientiarum? 

11.  Describe  the  humanistic  reaction  in  logic,  and  how  does 
it  affect  our  view  of  the  subject? 

12.  In  what  two  ways  do  logic  and  psychology  differ  from 
one  another? 

13.  What  two  meanings  may  be  given  to  the  term  art? 

14.  Is  logic  an  art  as  well  as  a  science?     Explain. 

15.  Summarise  the  various  definitions  of  logic  in  this  chap- 
ter, and  state  clearly  the  points  of  view  from  which  these 
definitions  are  made. 

EXERCISES 

1.  Point  out   the   subject-matter   in   the   case   of   any   six 
subjects  with  which  you  may  be  acquainted. 

2.  Show  the  relation  that  thought  has  to  each  of  the  sub- 
jects chosen  for  your  answer  to  the  previous  question. 

3.  Cite   concrete   instances   of  the   way   that  thought   be- 
comes  a   problem   in   the  pursuit   of  various   kinds   of 
knowledge. 

4.  Illustrate   how   observation   of   the   ordinary  modes   of 
conversation   may   advance   our   knowledge  of  the   log- 
ical processes. 

5.  Use  concrete  examples  to  show  the  limitations  to  which 
logic  would  be  subject  if  it  confined  itself  to  the  study 
of  the  scientific  mind. 

6.  Give  instances  of  the  practical  value  that  is  claimed  for 
an  acquaintance  with  logical  doctrine. 


CHAPTER  II 

THE   JUDGMENT 

The  Meaning  of  Thought.  Before  carrying  our 
study  of  the  logical  character  of  the  thought  proc- 
esses, begun  in  the  last  chapter,  into  greater  detail, 
we  wish  to  call  attention  to  two  simple  and  obvious 
considerations.  In  the  first  place,  we  may  observe 
that  the  objects  that  come  before  us  in  the  course 
of  our  experience  present  a  great  variety  of  charac- 
teristics. The  object  of  which  we  are  aware  may 
be  part  of  the  material  world,  —  the  starry  heavens ; 
it  may  be  part  of  the  common  human  life  that  today 
we  share  with  our  fellows,  —  the  rush  of  the  ambu- 
lance in  its  race  with  death;  it  may  be  part  of  the 
inner  individual  life,  —  the  secret  and  incommuni- 
cable thing  that  a  man  sees  when  he  sits  down  face 
to  face  with  himself.  In  short,  the  object  may  be 
anything  from  "the  choir  of  heaven  to  the  furniture 
of  earth ;"  but  whatever  it  is,  it  is  an  object  because, 
and  in  so  far  as,  we  have  experience  of  it.  We  shall 
use  the  term  object,  then,  to  denote  that  of  which 
we  have  experience,  without  respect  to  the  kind  of 
object  it  is,  or  the  kind  of  experience  in  and  through 
which  it  may  be  said  to  exist.  But  this  leads  to  a 
second  remark.  There  are,  as  we  intimated  just 
now,  a  variety  of  ways  in  which  we  experience,  or 
react  to,  or  are  aware  of  objects.  The  terms  per- 
ception, memory,  imagination,  feeling,  volition,  are 

(24) 


THE   JUDGMENT  25 

the  names  of  some  of  the  more  familiar  ways  of 
reacting  to  objects.  Thus  we  may  perceive  an 
object,  or  remember  it,  or  imagine  it,  or  be  affected 
pleasantly  or  unpleasantly  by  it,  or  do  something 
because  of  it.  All  these  are,  of  course,  familiar 
experiences,  and  we  do  not  need  to  be  psychologists 
to  be  aware  of  the  fact  that  the  object  assumes  a 
somewhat  different  character  for  the  different  activ- 
ities through  which  it  is  experienced.  That  is  to 
say,  the  object  as  we  perceive  it,  or  remember  it, 
or  imagine  it,  or  are  pleasantly  or  unpleasantly 
affected  by  it,  or  do  something  because  of  it,  has  a 
slightly  altered  aspect  in  these  several  modes  of 
reacting  to  it. 

Now  it  will  probably  help  us  to  understand  the 
problems  of  this  chapter  if,  at  the  outset,  we  observe 
that  the  recognition  of  this  implication  of  objects 
in  all  or  most  of  our  conscious  processes  has  led  to 
a  certain  looseness  in  our  use  of  the  term  thought. 
By  some,  especially  among  the  psychologists,  thought 
is  the  name  that  has  been  employed  to  denote  the 
various  kinds  of  mental  processes,  —  perception, 
imagination,  feeling,  desire,  emotion,  etc.  James, 
for  example,  speaks  of  the  'stream  of  thought/  a 
phrase  in  which  the  term  thought,  as  he  tells  us,  is 
used  for  "every  form  of  consciousness  indiscrim- 
inately." In  a  somewhat  more  restricted  sense,  the 
term  thought  or  cognition  is  used,  in  distinction 
from  feeling  and  conation  or  striving,  with  which 
it  is  intimately  associated,  as  the  name  for  one  of 
the  ultimate  modes  of  consciousness.  It  appears  in 


26  A  TEXT-BOOK   OF  LOGIC 

this  sense  in  the  writings  of  Stout  and  Ladd.  When 
employed  with  this  meaning,  it  denotes  all  those 
mental  activities,  such  as  perception,  memory,  con- 
ception, etc.,  in  which  we  are,  in  one  way  or  another, 
concerned  with  the  nature  of  objects.  "It  covers," 
as  Stout  says,  "all  modes  and  degrees  of  being  aware 
of  or  cognisant  of  an  object."  A  still  more  special- 
ised use  of  the  term  is  that  which  limits  its  appli- 
cation to  those  processes  whereby  we  designate 
objects  merely  as  the  objects  that  are,  at  the  present 
moment,  under  consideration.  To  think,  to  use 
James'  definition  of  conception,  with  which  the  term 
thought  in  this  sense  is  practically  synonymous,  is 
to  "identify  a  numerically  distinct  and  permanent 
subject  of  discourse;"  to  mark  it  off  from  other 
objects,  and  to  make  it  the  bearer  of  whatever  attri- 
butes or  relations  that  our  'thoughts-about'  it  may 
show  that  it  actually  possesses. 

The  three  meanings  just  distinguished  of  the 
term  thought  are  doubtless  closely  connected  from 
the  psychological  point  of  view.  For  if  psychology 
be  regarded  as  "the  science  of  the  processes  whereby 
an  individual  becomes  aware  of  a  world  of  objects 
and  adjusts  his  actions  accordingly,"  and  it  is  so 
regarded  by  Stout,  it  is  perfectly  obvious  that  the 
several  mental  processes  must  be  viewed,  in  them- 
selves and  in  their  relations  to  one  another,  as  modes 
of  conscious  activity  which  further,  more  or  less 
directly,  that  acquaintance  with  objects  which  all 
the  three  statements  of  the  meaning  of  thought 
alike  emphasise.  We  need  not  consider  whether, 


THE   JUDGMENT  27 

and,  if  so,  in  what  sense  all  the  fundamental  mental 
processes  serve  the  purpose  of  establishing-  and  im- 
proving our  acquaintance  with  things;  whether,  for 
example,  the  so-called  affective  processes  are  cor- 
rectly interpreted  in  this  way.  It  will  be  enough 
if  we  recognise  that  certain  processes  can  be  grouped 
together,  and  can  be  regarded  as  having  for  their 
distinctive  function  the  discriminating  and  relating 
of  the  objects  of  experience.  If  we  approach  the 
problem  of  thought  from  this  point  of  view,  we  see 
that  the  term  thought,  in  the  second  and  third  mean- 
ings distinguished  above,  have  a  peculiarly  close 
relation.  According  to  the  second  meaning,  thought 
is  a  continuous  process  which,  beginning  in  percep- 
tion, culminates  in  what  the  psychologist  calls  judg- 
ment and  reasoning.  Without  denying  that  thought 
is  dependent  upon  the  more  elementary  processes  of 
perception,  the  third  meaning  limits  the  application 
of  the  term  to  the  later  processes  in  which,  more 
particularly,  we  acquire  what  was  described  in  the 
previous  chapter  as  'knowledge-about'  objects.  For 
the  one,  thinking  is  the  name  for  a  process  in  which 
perception,  memory,  imagination,  conception  and 
judgment  may  be  found  to  function;  for  the  other, 
it  is  a  name  by  which  conception  and  judgment  are 
specifically  signified.  In  whichever  of  these  two 
contrasted  senses  the  term  is  used,  each  implies, 
what  is  undoubtedly  the  fact,  that  there  is  no  unique 
faculty  of  thought,  that  thought  is  a  complex  process 
in  which  a  number  of  mental  activities  combine  to 
give  us  a  knowledge  of  objects,  and  that,  while  some 


28  A  TEXT-BOOK   OF  LOGIC 

of  these  activities  enable  us  to  identify  distinct  and 
permanent  subjects  of  discourse,  others  carry  us 
beyond  this  to  the  knowledge  of  a  system  of  existing 
things  in  which  numerous  terms  and  relations  are 
discernible. 

Judgment  and  Thought.  Now  when  we  consider 
the  subject  of  thought  from  the  standpoint  of  logic, 
it  is  in  the  third  of  the  meanings  already  distin- 
guished that,  in  the  main,  we  shall  use  the  term. 
Thought  will  thus  signify  the  processes  of  judgment 
and  reasoning,  those  processes  in  which  the  cogni- 
tive process  as  a  whole  culminates.  Logic,  that  is 
to  say,  is  particularly  interested  in  the  terminus 
ad  quern  of  the  thought-process,  in  the  goal  toward 
which  our  desire  for  knowledge  points;  and  it 
studies  the  process  of  reaching  the  goal  only  when 
a  knowledge  of  such  process  enables  it  to  determine 
the  nature  and  grounds  of  the  validity  that  is 
claimed  for  thought.  Thinking  thus  comes  to  be 
regarded  by  logic  as  having  a  character  which  is 
liable  to  escape  notice  so  long  as  we  keep  strictly  to 
the  psychological  point  of  view,  —  the  character  of 
assertion.  And  in  order  to  give  prominence  to  this 
feature  of  thought,  logicians  are  more  apt  to  speak 
of  judgment  than  they  are  of  thought.  Thinking, 
as  we  have  seen,  is  a  mental  process  in  which  the 
psychologist  distinguishes  a  number  of  constitutive 
processes,  —  perception,  memory,  etc.  Judgment, 
as  it  is  used  by  the  logician,  regards  the  thought 
process  as  being  concerned  with  the  specification 
of  a  content,  the  assertion  of  which  is  logically  the 


THE   JUDGMENT  29 

characteristic  thing  about  a  judgment.  The  content 
of  the  thought  process  is  taken  up  by  the  judgment 
and  constituted  the  subject-matter  of  assertion. 
Thus  the  experience,  say,  of  red  calls  from  the  psy- 
chologist the  statement  that,  like  all  sensational 
experiences  red  cannot  be  described,  but  must  be 
experienced  if  any  one  is  to  know  what  the  word 
signifies,  that  it  is  produced  by  the  action,  on  the 
rods  and  cones  of  the  retina,  of  ether  waves  of  a 
certain  length,  and  that  these  changes  are  continued, 
by  way  of  the  optic  nerve,  in  a  manner  that  is  little 
understood,  to  the  occipital  lobe  which  is  the  cortical 
centre  of  the  visual  consciousness.  For  the  logician, 
the  particular  patch  of  colour  called  red  merely 
exists,  and  the  acknowledgment  of  it  as  existing, 
by  the  individual  who  experiences  it,  is  what  is 
meant  by  assertion  or  judgment.  The  red  is  the 
content  of  the  processes  which  are  described  by  the 
psychologist,  and  it  is  this  content  that  is  asserted 
as  the  subject-matter  of  the  judgment.  Whatever, 
then,  exists  as  content  of  thought,  may  become  the 
subject-matter  of  a  judgment;  and  we  may,  there- 
fore, define  a  judgment,  broadly,  as  an  assertion  of 
the  qualities  and  relations  of  the  object  of  thought. 
A  word  or  two  may  be  necessary  at  this  point 
to  guard  against  a  possible  misunderstanding  of 
what  is  meant  by  assertion  as  the  central  fact  of 
the  logical  judgment.  In  current  usage,  to  assert 
means  to  express  in  words  the  thoughts  and  opin- 
ions that  we  entertain  about  things.  It  is  commonly 
employed  as  the  equivalent  of  'to  say  something.' 


30  A   TEXT-BOOK   OF  LOGIC 

In  logic,  assertion  has  nothing  to  do  with  speech. 
We  may,  of  course,  express  what  we  assert,  but 
we  can  assert  without  putting  into  words,  or  into 
any  other  set  of  social  symbols,  the  qualities  and 
relations  of  the  object  of  thought.  The  question  we 
are  now  considering,  moreover,  has  nothing  to  do 
with  the  problem  whether,  as  individuals,  we  can 
think  without  words.  It  is  a  simpler  matter  than 
that;  and  all  that  we  say  is  that  no  one,  merely 
because  he  judges,  is  bound,  in  order  to  give  his 
judgment  the  character  of  assertion,  to  put  into 
language  the  truth  or  fact  that  his  judgment  em- 
bodies. On  the  contrary,  by  assertion  we  mean  the 
attitude  of  mind  in  which,  for  that  mind  itself, 
there  consciously  exists  such  an  acquaintance  with 
an  object  that,  in  itself  and  its  relations,  it  is  dis- 
tinguished from  other  objects  with  which  it  occurs 
in  a  common  field  of  knowledge.  For  example,  I 
may  be  looking  over  a  collection  of  curiosities  that 
a  friend  has  accumulated  from  the  four  corners  of 
the  earth.  I  look  at  the  objects  one  after  the  other, 
and  find  that  each  is  a  strange  and  unintelligible 
thing,  and,  as  I  put  it  back  into  its  place,  it  is  soon 
lost  in  the  mass  of  the  other  strange  and  unintel- 
ligible things.  If,  however,  I  should  find  in  the  col- 
lection an  object  that  is  familiar,  there  would  be, 
under  the  circumstances  supposed,  a  mental  tang 
and  'feel'  toward  it  that  would  make  it,  as  I  put 
it,  too,  back  in  its  place,  stand  out  from  the  rest,  - 
its  identity  would  not  get  lost  in  the  multitude  of 
strange  things.  What  makes  the  difference  in  this 


THE   JUDGMENT  31 

case  is  my  mental  attitude  toward  it,  —  a  mental 
attitude  that,  in  this  instance,  is  called  recognitive 
judgment.  In  logic,  the  mental  attitude  in  which 
we  find  the  characteristic  feature  of  the  judgment 
is  described  as  assertion.  Whenever  we  judge  we 
assert,  and  whenever  we  assert  we  put  marks  upon 
the  objects  that  come  before  us  by  which  they  attain 
unique  distinction. 

Other  Mental  Attitudes  Akin  to  Judgment.  It  may 
help  to  emphasise  the  assertive  character  of  the 
judgment  if  we  distinguish  certain  other  attitudes 
which,  like  assertion,  have  received,  in  the  develop- 
ment of  language,  definite  verbal  forms.  Judgments, 
it  should  be  observed,  are  always  expressed  in  the 
indicative  mood,  and  what  they  assert  is  always  true 
or  false.  On  the  other  hand,  interrogatives,  imper- 
atives, optatives,  and  exclamations  do  not  assert, 
and  therefore  are  not  judgments,  but  express  either 
an  inquiry,  a  command,  a  wish,  or  an  emotion.  Of 
the  wishes  that  optatives  express  we  can  say  that 
they  are  reasonable  or  unreasonable.  The  com- 
mands of  imperatives  can  only  be  obeyed  or  dis- 
obeyed. Our  interrogatives  formulate  inquiries  and 
call  for  an  answer.  Exclamations  are  word  ges- 
tures that  express  our  emotional  attitudes  toward 
situations.  But  while  interrogatives,  imperatives, 
optatives,  and  exclamations  are  not  judgments,  they 
imply  attitudes  of  mind  which,  if  asserted,  would 
be  judgments.  The  rhetorical  question,  'Is  thy  ser- 
vant a  dog?'  doubtless  implies  an  assertion,  and  is 
equivalent  to  'Thy  servant  is  not  a  dog.'  But  not 


32  A  TEXT-BOOK  OF  LOGIC 

only  the  rhetorical,  but  any  question  may  be  inter- 
preted in  a  similar  way.  For  to  ask  a  question 
would  be  meaningless  unless  we  thereby  implied 
that  something  can  be  asserted  of  its  subject,  and 
it  is  to  this  something  that  the  question,  in  a  general 
way,  points.  If,  for  example,  I  ask,  'Is  that  a  fire?' 
I  imply  that  it  is  a  fire,  but  not  in  the  way  that 
would  warrant  me  in  asserting  it  as  a  fact.  With 
imperatives  the  case  is  different.  'Come,'  'Do  this,' 
cannot  be  said  to  be  either  true  or  false,  and  they 
imply  assertion  only  if  imperatives  are  indicated 
actions  that  have  reference  to  a  situation  which 
they  either  help  or  hinder.  Imperatives,  that  is,  get 
their  meaning  from  a  context  that  exists  in  the 
mind  of  the  person  issuing  the  command,  a  context 
which  must  rely  for  its  development  upon  the  action 
of  the  person  to  whom  the  command  is  addressed. 
The  implied  judgment,  therefore,  may  be  thrown 
into  the  hypothetical  form  thus:  'If  you  do  the 
thing  commanded,  such  and  such  things  will  happen.' 
Commands,  that  is,  are  abbreviated  antecedents  of 
hypothetical  judgments.  Optatives  express  a  desire 
for  some  state  or  condition  which  is  thought  of  as 
possible,  though  not,  at  the  moment  the  wish  is 
entertained,  as  actual.  They  imply  the  assertion 
of  definite  objects  as  the  objects  of  desire.  In  this 
way  we  must  interpret,  for  example,  'Would  that  I 
were  dead!'  It  implies  that  'to  be  dead  at  this 
moment'  is  really  a  desired  object.  Such  exclama- 
tions as  'Absurd!'  'Impossible!'  are  predicates  of 
implied  judgments,  and  by  them,  besides  expressing 


THE   JUDGMENT  33 

our  personal  attitudes,  we  are  also  characterising 
situations. 

Judgment  and  Groundless  Statements.  Before 

proceeding  to  develop  other  features  of  the  judg- 
ment, as  this  has  been  defined  in  the  previous  sec- 
tions, there  is  a  class  of  statements  about  which  we 
are  called  upon  to  say  something  if  only  for  the 
sake  of  clearing  our  exposition  of  the  subject  under 
discussion  from  unnecessary  ambiguity.  We  have 
seen  that  assertion  is  the  main  characteristic  of 
judgment,  and  that  what  a  judgment  asserts  is  some 
quality  or  relation  of  the  objects  about  which  we 
think.  It  would  seem  quite  obvious,  therefore,  that 
unless  we  think  about  some  object  or  other,  there 
can  be,  for  us,  no  such  thing  as  judgment.  Judg- 
ment implies  thought,  and  thought  implies  some- 
thing thought  about. 

In  contrast  to  judgment,  as  thus  understood,  we 
are  confronted  with  a  class  of  statements  which 
simulate  judgments,  but  which  fall  short  of  being 
true  judgments  because  they  are  not  based  on  the 
thinking  of  the  person  who  makes  them.  We  may 
cite  in  illustration  not  only  the  parrot-like  state- 
ments of  the  class-room  recitation,  but  the  ill- 
informed  and  often  misleading  expressions  of  opin- 
ion that  many  of  us  allow  ourselves  to  make  with 
confidence  on  all  sorts  of  subjects  about  which  we 
know  relevantly  nothing.  The  certainty  that  at- 
taches to  such  statements  has  little  or  nothing  to  do 
with  their  subject-matter;  it  usually  rests  upon  the 


34  A  TEXT-BOOK   OF  LOGIC 

confidence  we  have  in  'authority'  of  some  kind  or 
other.  For  instance,  students  rarely  call  in  question 
the  statements  they  find  in  their  text-books,  and 
consequently  they  are  ready  to  state  as  true  any- 
thing they  read  in  them  for  no  better  reason  than 
that  it  is  'in  the  book.'  Indeed,  most  of  us  entertain, 
and  express  to  others,  beliefs  that  are  based  solely 
upon  statements  we  have  read  in  some  magazine  or 
newspaper,  or  have  heard  in  a  public  address  or  in 
private  conversation.  To  communicate,  in  this  way, 
the  opinions  of  others  is  doubtless  a  valuable  social 
function,  but  the  statements  in  which  another's 
views  are  given  currency  should  not  be  confused 
with  judgments  in  the  sense  in  which  this  term  has 
been  defined.  We  may,  for  want  of  a  better  word, 
distinguish  these  statements  as  groundless  asser- 
tions, for  what  enables  us  to  distinguish  them  from 
true  judgments  is  the  fact  that,  in  respect  of  the 
latter,  we  are  always  more  or  less  conscious  of  the 
reasons  for  what  the  judgment  asserts.  Our  judg- 
ments are,  as  it  is  said,  grounded  judgments,  and 
the  grounds  of  the  judgment  are  the  reasons  that 
thought  can  give  for  the  particulars  asserted  by  the 
judgment.  For,  as  we  have  seen,  the  asserted  par- 
ticulars are  always  what  thought  reveals  as  true  of 
the  subject  thought  about. 

The  distinction  that  we  have  drawn  in  this  sec- 
tion between  groundless  statements  and  judgment 
corresponds,  in  a  general  way,  to  that  which  appears 
in  the  history  of  Greek  speculation  as  the  distinction 
between  'opinion'  and  'knowledge.' 


THE    JUDGMENT  35 

Practical  and  Theoretical  Aspects  of  Thought. 
Whether  we  use  the  term  thought  in  the  broadest 
of  the  meanings  already  distinguished,  or  in  one  of 
its  more  restricted  senses,  it  is  undoubtedly  true 
that  we  cannot  fully  describe  the  experience  that 
the  term  denotes  without  recognising  the  fact  that, 
along  with  those  differentiations  which  the  object 
of  thought  undergoes,  for  example,  in  perception, 
in  ideal  representation,  and  in  ideational  thought, 
tendencies  of  a  practical  sort  are  aroused  which  not 
only  accompany  the  thinking  process,  but,  in  part, 
give  it  the  character  and  direction  which  it  undoubt- 
edly possesses.  Thus  the  psychologists  have  been 
accustomed  to  recognise  that  instinctive  impulses 
are  present  in  perception  which  tend  to  place  the 
percipient  subject  in  relation  to  external  objects; 
that  in  ideal  representation  active  tendencies  of  the 
kind  called  desires  are  directed  toward  objects 
which,  not  being  actually  present,  are  held  before 
consciousness  as  an  end  to  be  realised;  and  that  in 
ideational  thought  the  process  of  generalisation  for- 
mulates ideals  which  are  sometimes  of  so  complex 
a  character  that,  while  they  may  become  the  objects 
of  individual  desire,  they  are  attainable  only  as  the 
result  of  social  cooperation.  Whether,  therefore,  in 
its  simpler  or  more  complex  forms,  thought  seems 
to  have,  not  only  an  aspect  which  is  directly  con- 
cerned with  the  definition  of  an  object,  a  theoretical 
aspect,  but  also  a  practical  aspect,  a  certain  conative 
tendency  whose  function  it  is  to  direct  the  process 


36  A  TEXT-BOOK   OF  LOGIC 

of  thinking  and  to  give  its  content  a  definite  charac- 
ter and  objective. 

Relevant  Assertion.  From  the  point  of  view  we 
have  now  reached,  we  may  indicate  certain  features 
of  the  logical  judgment  which  correspond,  in  a  gen- 
eral way,  to  this  distinction  in  the  nature  of  think- 
ing itself.  The  function  of  judgment  we  have  said 
is  assertion.  We  have  now  to  point  out  that  when- 
ever assertion  satisfies  the  logical  conditions  of 
truth,  and  is  not  mere  or  groundless  assertion,  it  is 
seen  to  have  two  characteristics  both  of  which  are 
included  under  the  single  term  'relevant.'  More 
explicitly  stated,  judgments,  in  the  logical  sense  of 
that  term,  are  always  relevant  assertions,  and  their 
relevancy  is  based  upon,  and  is  the  logical  expression 
of,  the  theoretical  and  practical  aspects  of  the 
though  process  which  were  indicated  above.  Judg- 
ments, in  other  words,  always  refer  to  some  object, 
and  fulfill  some  need  of  the  person  asserting  the 
judgment.  Whenever  they  do  either  or  both  of  these 
things,  our  judgments  are  said  to  be  relevant  asser- 
tions. Briefly  stated,  judgments  are  assertions  that 
are  relevant  (1)  to  the  motives  that  operate  to 
produce  them,  and  (2)  to  the  material  by  which 
they  are  called  forth  and  to  which  they  refer. 

To  consider  the  first  meaning  of  relevancy,  that 
which  refers  to  the  motives  that  operate  to  produce 
our  judgments,  we  may  say  that  this  is  concerned 
with  the  reasons  why  any  one  judges  at  all.  If, 
then,  it  were  asked  why  any  one  judges,  the  answer 
would  be  that  one  cannot  'get  along'  without  it.  In 


THE   JUDGMENT  37 

a  broad  way,  the  life  of  thought  is  based  in  and 
grows  out  of  our  practical  needs.  As  an  illustration 
of  what  this  statement  means,  we  may  refer  to  the 
development  of  agriculture  in  the  history  of  civil- 
isation. Before  agriculture  had  become  one  of  the 
institutions  of  human  society,  men  no  doubt  were 
confronted  with  the  problem  of  food  supply,  and 
they  met  this  problem  in  a  way  that  was  fairly 
satisfactory  until  the  accumulation  of  various  forms 
of  wealth  made  a  predatory  and  wandering  life  both 
irksome  and  unprofitable.  When,  for  instance,  the 
domestication  of  animals  had  become  an  accom- 
plished fact,  this  not  only  made  a  wandering  life 
more  difficult,  but  it  also  exposed  the  primitive  com- 
munity to  greater  loss  through  drought,  long  jour- 
neys, and  marauding  attacks  from  hostile  and  mer- 
cenary tribes.  But  unless  fruits  and  cereals  could 
be  domesticated,  as  animals  had  been,  there  was 
before  the  primitive  community  the  necessity  of 
seeking  food  where  it  grew,  whatever  the  risks  and 
losses  that  might  be  incurred.  Now  it  takes  but  a 
little  imagination  to  see  that  the  great  difficulties 
that  beset  tribes  advancing  from  a  wandering  to  a 
settled  mode  of  life  would  act  as  a  stimulus  to  their 
thought,  and  would  engage  their  thought  in  the 
direction  of  these  difficulties  themselves.  It  may 
seem  to  us  who  have  grown  up  under  settled  con- 
ditions of  life  a  simple  matter  to  perceive  the  prob- 
lem and  the  solution  of  which  it  was  capable.  But 
before  the  food  supply  of  man  and  beast  could  be 
raised,  within  a  restricted  area,  by  man's  efforts 


38  A   TEXT-BOOK   OF  LOGIC 

from  seeds,  there  was  required  exactly  that  develop- 
ment of  the  thought  processes  which  the  mainte- 
nance of  the  institution  of  agriculture  calls  for  at 
the  present  day.  What,  therefore,  we  may  say  is 
that  the  principle  of  this  illustration,  namely,  that 
our  needs  stimulate  the  judging  activity  and  direct 
it  toward  an  understanding  of  whatever  threatens 
the  satisfaction  of  these  needs,  is  capable  of  indefi- 
nite extension ;  and  that  the  incentives  to  knowledge 
become  more  numerous  and  diverse  as,  with  the 
growth  in  complexity  of  our  social  life,  obstacles 
are  multiplied,  and  needs  increase  in  number  or 
change  their  form.  Thus,  over  the  whole  course 
of  our  experience,  thought  not  only  interprets  the 
environment,  but  determines  the  particular  adjust- 
ments that,  under  change  of  environment,  are  neces- 
sary if  the  varying  needs  of  life  are  to  be  met. 

The  relevancy  of  our  judgments  to  the  varying 
needs  by  which  they  are  called  forth  may  be  further 
illustrated,  and,  for  this  purpose,  let  us  suppose 
that  we  have  a  hundred  books,  and  that  our  problem 
is  what  we  are  going  to  do  with  them.  It  is  very 
probable,  first,  that  we  shall  want  to  have  them  all 
in  one  place.  Within  the  space  allotted  to  them,  we 
are  likely  to  arrange  them  under  some  scheme  of 
classification,  —  authors,  subjects,  or  what  not. 
Now  why  do  we  do  this?  Is  it  needless?  By  no 
means.  We  are  simply  obeying  in  our  manner  of 
dealing  with  the  books  a  fundamental  need  for 
order.  But  what  particular  order  we  impose  upon 
the  books  will  depend  upon  the  particular  form  that 


THE   JUDGMENT  39 

the  demand  assumes.  Thus,  in  the  first  instance, 
we  bring  all  the  books  together  in  one  place;  place 
is  the  principle  of  our  classification.  In  the  second 
instance,  we  have  carried  the  matter  further,  and 
have  arranged  the  books,  let  us  say,  according  to 
subjects,  —  subject-matter  is  a  more  specialised 
form  of  the  need  for  order  which  operates  through- 
out all  our  classifications.  But  if  it  is  asked  why 
any  order  is  necessary,  we  can  only  say  that  when 
classified  objects  are  more  easily  handled  and  used. 
The  point  of  the  illustration  is  that,  when  we  have 
to  deal  with  a  hundred  books,  we  are  bound  to  think 
about  the  books  in  terms  of  our  interest  in  them. 
Thus  the  first  classification  according  to  place  might 
be  satisfactory  to  the  housekeeper  whose  interest  in 
the  books  is  aesthetic,  —  as  articles  of  furniture  in  a 
room.  The  classification  according  to  author  would 
satisfy  the  interests  of  the  man  whose  manner  of 
speaking  about  books  is,  'Oh,  yes,  I  have  Dickens, 
Eliot,  Thackeray,  etc.'  The  scholar's  interest  is 
most  likely  to  be  met  by  the  arrangement  according 
to  subjects.  In  each  case,  what  we  think  about  the 
books,  —  whether  as  articles  of  furniture,  or  as  the 
works  of  such  and  such  authors,  or  as  dealing  with 
given  subjects,  —  depends  upon  the  interest  we  have 
in  them.  And  what  is  true  in  this  particular  in- 
stance is  true  in  every  case  of  judgment.  Our  judg- 
ments, in  a  word,  are  assertions  that  are  relevant 
to  the  interests  out  of  which  they  are  born. 

The  foregoing  statement  and  illustrations  of  the 
conditions  under  which  the  judging  activity  comes 


40  A  TEXT-BOOK   OF  LOGIC 

into  play  indicate  clearly  enough  what  is  meant  by 
the  practical  nature  of  all  our  thinking.  But  be- 
cause the  word  practical  is,  in  ordinary  speech,  so 
intimately  associated  with  the  getting  of  material 
goods,  or  with  the  removal  of  material  hindrances, 
the  exact  meaning  of  the  statement  that  all  judgment 
is  conditioned  by  the  presence  of  practical  needs  is 
liable  to  be  given  too  narrow  an  interpretation.  By 
a  practical  need,  it  is  true,  we  mean  one  that  is  con- 
cerned with  getting  an  anticipated  good,  or  with 
removing  a  present  hindrance  to  further  goods. 
But  the  goods  in  question  need  not  be  material,  and 
in  many  cases  are  not  material.  We  have  no  wish 
to  deny  that  man  is  an  economic  animal,  and  that 
what  we  call  property  is  based  in  and  grows  out  of 
his  need  for  'things/  But  it  is  no  less  true  that 
man  is  a  social  animal,  and  that  the  various  organ- 
isations in  which  he  is  associated,  —  the  family,  the 
shop,  the  club,  etc.,  —  have  their  foundation  in  the 
needs  which  prompt  men  to  associate  with  their 
kind.  The  social  is,  no  less  than  the  economic,  a 
practical  need.  A  similar  line  of  remark  applies  also 
to  our  science,  art,  and  religion.  There  are,  doubt- 
less, intellectual,  emotional,  and  volitional  needs, 
complex  in  their  nature,  and  variously  combined  in 
the  instances  just  given,  which  impel  men  to  seek 
their  satisfaction  in  the  formulation  of  the  objects 
to  which  these  needs  point.  Over  the  whole  range 
of  life,  then,  situations  are  constantly  arising  in 
which  unsatisfied  demands  impel  us  to  think,  and 
to  think  with  reference  to  these  demands.  Nowhere 


THE   JUDGMENT  41 

can  this  practical  aspect  of  the  judging  activity  find 
more  or  more  pertinent  illustration  than  in  a  study 
of  the  ways  in  which  the  human  race  has  advanced 
in  the  arts  of  civilised  life.  But  to  bring  the  truth 
of  this  view  home  to  ourselves,  we  need  only  to  ask 
if  we,  as  individuals,  ever  think  when  the  situations 
in  which  we  find  ourselves  are  entirely  satisfactory. 
Even  a  student,  very  often,  will  not  think  until  a 
failure  stares  him  in  the  face. 

Turning  now  to  the  second  meaning  of  relevancy, 
we  may  say  that  judgments  are  assertions  about 
the  material  by  which  they  are  called  forth  and  to 
which  they  refer.  In  the  development  of  knowledge, 
our  interests  never  become  so  one-sided  that  our 
judgments  are  freed  from  the  control  of  the  mate- 
rial through  which  these  interests  are  to  receive 
their  satisfaction.  If,  for  instance,  we  were  con- 
scious of  nothing  but  compelling  interests,  be  those 
interests  psychologically  never  so  definite,  or  if  we 
were  moved  by  a  vague  catholicity  of  mind  that 
went  out  to  everything  in  general,  but  took  hold  on 
nothing  in  particular,  judgment  would  be  impos- 
sible. There  are  states  of  mind  that  correspond 
more  or  less  closely  to  those  just  described,  states 
that  are  definite  as  to  interests  but  indefinite,  vague, 
or  empty  as  to  their  objects;  and  others  that  are 
vague  and  indefinite  in  both  respects;  but  no  one 
would  think  of  calling  these  states  cognition,  or  the 
reactions  they  may  involve  judgments.  What  we 
aim  at  in  the  judgment  is  to  characterise  an 


42  A  TEXT-BOOK   OF  LOGIC 

object  in  such  a  way  that  it  becomes  better 
known.  The  study  of  the  judgment,  therefore,  is 
a  study  of  the  relation  of  thought  to  its  object. 
Now,  when  one  attempts  to  study  the  relation  in 
which  thought  stands  to  its  object,  one  is  partic- 
ularly prone  to  two  kinds  of  error.  In  the  first 
place,  he  is  apt  to  think  of  the  mind  as  a  passive 
mirror  that  reflects  indifferently  whatever  is  held 
up  before  it.  That  is  to  say,  he  is  liable  to  overlook 
the  presence  in  all  knowledge  of  the  interest  factor 
of  which  we  have  already  spoken.  If,  however,  he 
escapes  this  pitfall,  he  is  prone  to  go  to  the  other 
extreme  and  think  of  the  mind  as  a  magic  mirror 
that  transforms  out  of  all  likeness  to  their  own 
nature  the  objects  that  pass  in  front  of  it.  That  is 
to  say,  he  is  liable  to  overlook  or  underestimate  the 
material  factor  to  which  attention  is  now  being 
directed.  Interests,  as  we  have  seen,  do  make  our 
judgments  significant;  but  if  they  are  to  reach  truth 
they  must  also  be  brought  under  the  control  of 
objective  fact.  No  judgment  can  be  regarded  as 
having  reached  truth  which  does  not  open  to  us  the 
nature  of  the  object  about  which  it  undertakes  to 
inform  us.  The  fact,  therefore,  about  the  judgment 
is  that,  within  the  sphere  of  the  interests  that 
stimulate  the  judging  process,  the  character  of 
our  assertions  is  limited  by  the  nature  of  the  mate- 
rial or  subject  with  which  we  are  dealing.  For 
example,  in  writing  this  section  of  logic,  I  am 
prompted  by  the  desire  to  write  in  such  a  way  that 
the  student  who  reads  shall  be  able,  with  ordinary 


THE   JUDGMENT  43 

attention,  to  understand  the  doctrine.  But  what 
the  doctrine  is  does  not  depend  upon  this  interest; 
what  I  say  must  be  true  of  the  subject  we  are  dis- 
cussing. However,  this  must  be  said,  that  what  I 
include  and  what  I  omit,  what  form  the  sentences 
take,  and  what  illustrations  are  used,  are  deter- 
mined by  the  purpose  and  needs  the  section  is  in- 
tended to  serve.  I  cannot  say  anything  I  please 
about  the  judgment,  but  I  can  examine  it  to  see 
how  far  it  lends  itself  to  the  satisfaction  of  the 
interests  that  lead  me  to  write  about  it.  We  may 
take  any  other  illustration  we  please,  and  the  same 
thing  will  be  found  true.  The  difference,  for  ex- 
ample, between  history  and  romance,  other  things 
being  equal,  is  the  difference  between  the  way  the 
historian  and  the  novelist  feel  themselves  bound  by 
the  character  and  order  of  the  occurrences  which 
they  narrate.  The  historian's  purpose  is  to  describe 
a  complex  social  situation  as  it  actually  existed,  and 
to  develop  the  consequences,  in  the  way  of  cause  and 
effect,  of  the  situation  thus  depicted.  The  novelist's 
treatment  of  the  same  material  is  much  freer  from 
the  control  of  the  objective  events  within  which,  as 
in  a  framework,  his  romance  is  made  to  move.  But 
it  is  only  in  the  former  of  these  two  cases  that  truth 
is  the  aim;  the  relative  unimportance  of  this  aim 
in  the  novel  accounts  for  the  looser  handling  of  the 
historical  material.  We  may,  therefore,  conclude 
that  interest  or  purpose  sustains  and  directs  the 
whole  process  in  which  our  judgments  are  formed, 
and  that  what  the  judgment  asserts,  since  all  judg- 


44  A  TEXT-BOOK   OF  LOGIC 

ments  claim  to  be  true,  must  derive  its  character 
from  the  material  which  constitutes  the  subject- 
matter  of  the  process  of  judgment. 

The  Interest  Factor  in  Knowledge.  In  the  pre- 
ceding section,  we  have  seen  that  judgments  are 
assertions  that  are  relevant  to  the  interests  or  pur- 
pose of  the  person  who  judges,  and  also  to  the 
material  or  body  of  facts  which,  in  the  judgment, 
receive  a  particular  characterisation.  Now  it  will 
serve  to  further  emphasise  this  distinction,  if  we 
call  attention  more  particularly  to  the  way  in  which 
these  factors  of  knowledge  are  related  to  one  an- 
other. We  may  in  general  distinguish  two  cases. 
There  is  first  the  case  in  which  our  interest  in  the 
objects  which  we  are  led  to  observe  is  extrinsic  to 
the  objects  themselves,  and,  secondly,  the  case  in 
which  it  is  primarily  intrinsic. 

To  consider  the  former  case,  we  may  remark 
that  we  are  often  led  to  observe  and  make  asser- 
tions about  objects,  not  because  of  any  particular 
interest  in  the  objects  themselves,  but  because  of 
the  relation  in  which  these  objects  stand  to  other 
objects  in  which  we  are  interested.  Let  us  take 
as  an  example  my  observation  of  the  shape,  colour, 
and  arrangement  of  the  roses  in  the  vase  that  stands 
upon  the  table  at  which  I  write.  It  is  true,  of 
course,  that  I  may  be  induced  to  observe  them,  and 
to  study  their  particular  characteristics  by  reason 
of  an  interest  that  is  rooted  in  my  knowledge  of 
floriculture.  But,  on  the  other  hand,  the  attention 
that  I  give  to  the  flowers  may  be  due,  for  example, 


THE   JUDGMENT  45 

to  my  interest  in  the  person  who  picked  them  and 
placed  them  where,  as  I  now  write,  they  become 
the  object  of  my  perception.  Or,  if  this  is  not  the 
fact,  my  interest  may  grow  out  of  my  liking  for  a 
patch  of  colour  of  any  kind,  or  for  the  particular 
combination  of  colours  that  the  flowers  present.  In 
the  former  of  these  suppositions,  the  interest  is 
social,  and  in  the  latter,  it  is  aesthetic.  In  in- 
stances like  these,  we  may  say  that  the  object 
sustains  an  interest  that  is  extrinsic  to  itself,  and 
gives  to  the  interest  a  longer  life  than  it  would 
otherwise  have.  If,  from  this  point  of  view,  we 
speak  of  the  flowers  at  all  we  should  say  that  they 
were  pretty,  —  a  judgment  it  is  true,  but  one  which 
expresses  one's  feelings  for  the  flowers  rather  than 
one  which  tells  anything  about  the  flowers  them- 
selves. Such  judgments  are  usually  called  value 
judgments,  —  judgments  which  express  the  value 
or  worth  of  the  objects  for  the  individual  expressing 
the  judgment.  We  express  multitudes  of  such  judg- 
ments in  the  course  of  our  lives,  and  of  a  great  deal 
that  is  noblest  and  best  in  our  experience  we  can 
speak  in  no  other  way.  The  student  will  find  that 
most  of  the  judgments  that  he  expresses  on  morals, 
art,  and  religion  are  what  are  called  value  judg- 
ments ;  judgments,  that  is  to  say,  that  are  stimulated 
by  interests  that  are  extrinsic  to  the  objects  about 
which  he  judges. 

If,  now,  we  consider  knowledge  in  the  more 
scientific  meaning  of  the  term,  we  shall  find  that 
here  the  interest  factor  is  intrinsic,  that  it  is 


46  A   TEXT-BOOK   OF  LOGIC 

grounded  in  the  object  in  a  way  we  have  seen  not 
to  be  the  fact  in  the  class  of  cases  just  studied. 
Scientific  interest,  in  other  words,  is  an  interest  in 
objects  for  their  own  sake.  Of  course,  it  is  some- 
times said  that  interest  or  purpose  is  altogether 
absent  from  our  scientific  activities,  and  that  it  is 
this  fact  that  distinguishes  science  from  all  other 
kinds  of  knowledge.  If  all  that  has  been  written 
about  the  disinterested  nature  of  scientific  study 
were  true,  science  would  have  been  destroyed,  before 
this,  at  the  hands  of  its  friends.  The  fact  is,  how- 
ever, as  our  study  of  the  nature  of  knowledge  has 
shown,  there  is  no  knowledge  which  does  not  spring 
from  some  form  of  human  interest.  It  is  not  true, 
therefore,  that  what  we  mean  by  science,  in  con- 
tradistinction to  what  is  not  science,  can  be  stated 
in  terms  of  its  freedom  from  interests  which 
direct  the  course  and  prescribe  the  goal  that  science 
aims  to  reach.  What  is  true,  on  the  negative  side, 
is  that  certain  kinds  of  interests  are  detrimental 
to  the  existence  of  science.  But  to  deny  the  useful- 
ness of  certain  kinds  of  interest,  is  certainly  a  very 
different  matter  from  denying  all  interest  whatever. 
For  science,  as  was  pointed  out  by  Plato  and  Aris- 
totle, would  have  no  existence  were  it  not  for  that 
curiosity  and  wonder  which  is  awakened  very  early 
in  all  of  us  by  the  changing  appearances  in  the 
course  of  nature.  It  is  this  curiosity  which,  when 
specialised,  is  the  source  of  scientific  interest,  and 
which,  in  its  developed  form,  is  an  interest  which 
centres  in  the  objects  which  it  prompts  us  to  study. 


THE   JUDGMENT  47 

In  other  words,  the  interest  which  is  the  motive  of 
scientific  effort  appears  in  the  form  of  a  desire  to 
comprehend  the  nature  and  relations  of  the  objects 
of  our  experience.  The  better  we  understand  these 
objects,  the  more  alive  does  our  interest  in  them 
become;  and  the  more  alert  this  interest,  the  more 
keen  do  we  become  in  our  study  of  these  objects. 
The  interest  and  the  object  of  scientific  work  are 
thus  keyed  to  each  other  in  a  way  that  makes  them 
mutually  supporting;  and  the  further  we  study 
their  relations,  the  clearer  does  it  become,  as  was 
intimated  above,  that  they  are  different  aspects  of 
a  single  process.  Scientific  interest,  then,  is  an 
interest  in  objects  for  their  own  sake;  it  is  an  in- 
terest that  prompts  us  to  ascertain  all  that  can  be 
truly  known  about  these  objects. 

The  Object  of  Judgment.  If  we  now  pass  from 
the  study  of  the  relations  of  interest  and  subject- 
matter  upon  which  we  have  been  dwelling,  and 
regard  the  judgment  as  an  assertion  about  its 
subject-matter,  certain  other  features  of  the  judg- 
ment come  into  view.  In  our  previous  discussions, 
we  have  had  occasion  to  specify  what  is  meant  by 
the  subject-matter  of  the  judgment,  and  this,  it  will 
be  remembered,  was  found  to  be  identical  with  what, 
from  the  psychological  point  of  view,  is  denominated 
the  content  of  thought.  Thought  and  judgment  are 
thought  and  judgment  about  some  thing.  Without, 
therefore,  the  challenge  of  some  thing  neither 
thought  nor  judgment  takes  place.  But  while 
thought  and  judgment  imply  the  existence  of  a 


48  A  TEXT-BOOK   OF  LOGIC 

subject,  neither,  in  the  strict  sense  of  these  terms, 
is  identical  with  the  existence  of  its  subject.  There 
seems  to  be,  therefore,  some  other  feature  of  the 
judgment  which  distinguishes  it  from  mere  aware- 
ness, and  it  is  this  feature  that  we  have  now  to 
consider. 

We  may  perhaps  bring  the  question  of  discussion 
distinctly  forward  by  the  aid  of  an  illustration. 
Let  it,  therefore,  be  supposed  that  I  am  gazing  out 
of  the  window  while  thinking  about  the  distinction, 
within  the  logical  judgment,  that  it  is  now  my  desire 
to  state.  I  turn  the  subject  about  which  I  am 
thinking  this  way  and  that,  experimenting  with  it 
until  my  interest  in  it  begins  to  wane.  What  I 
find,  under  the  supposed  conditions,  is  that  the 
more  interest  in  the  original  subject  wanes,  the 
more  insistently  do  factors  from  other  parts  of  my 
environment  obtrude  on  consciousness;  and  by  and 
by  I  find  myself  wholly  engaged  with  some  of  these, 
-the  sloping  hill  side,  the  frozen  lake,  and  the 
lively  company  of  girls  and  boys  skating  upon  its 
surface.  In  such  an  experience,  what  one  observes 
is  that  not  only  has  there  been  a  change  from  one 
subject  to  another,  from  a  logical  problem  to  a 
physical  object,  but  also  that  changes  of  another 
kind  have  accompanied  those  already  indicated.  The 
two  consecutive  contents  of  the  thought  processes, 
that  is  to  say,  have  been  followed  by  changes  in  the 
character  of  what,  in  each  instance,  is  asserted.  I 
do  not  find,  in  other  words,  that  what  I  am  thinking 
when  engaged  with  the  logical  problem  fits  in  with, 


THE   JUDGMENT  49 

or  can  be  carried  over  to,  the  scene  in  the  distance 
which  has  now  become  the  content  of  my  thought. 
Each  content  has  its  own  appropriate  set  of  asser- 
tions. To  assert  of  its  subject  significant  qualities 
and  relations  is  what  we  understand  to  be  the 
object  of  the  logical  judgment.  It  will  serve  to 
emphasise  the  distinction  between  the  subject  and 
the  object  of  judgment  if  we  recall  that  Bradley 
discriminates  in  the  judgment  between  what  he  calls 
the  'that'  and  the  'what.'  By  the  'that'  of  a  judg- 
ment we  may  mean  the  content  or  material  of  a 
thought  process,  that  is,  the  subject  of  the  judgment 
as  we  have  used  that  term.  By  the  'what'  may  be 
understood  the  complex  asserted  by  the  judgment. 
For  instance,  the  joyful  scene  upon  the  frozen  lake, 
of  an  illustration  already  used,  is  the  subject-matter 
of  any  judgment  that  I  may  make  about  it.  In 
Bradley 's  terminology,  it  is  the  'that'  of  the  judg- 
ment. If,  however,  I  assert  that  there  is  danger 
from  the  ice  because  of  a  thaw,  and  the  children 
should  be  warned,  this  would  be  the  object  or  the 
'what'  of  the  judgment,  the  complex  whole  that  it 
is  the  business  of  the  judgment  to  assert. 

More  recently  a  similar  distinction  has  been 
drawn  by  the  Austrian  psychologist,  Meinong. 
Meinong  insists  that  we  must  not  confuse  in  any 
act  of  judgment  that  concerning  which  we  judge, 
and  what  we  judge  about  it.  The  distinction  that 
is  thus  drawn  for  all  judgments  is  that  with  which 
we  are  familiar  in  the  case  particularly  of  legal 


50  ,        A   TEXT-BOOK   OF  LOGIC 

judgments.  Let  us  say  that  a  person  is  accused  of 
a  crime.  In  such  a  case,  we  may  ask,  What  is  it 
that  the  judge  and  jury  are  expected  to  judge?  In 
one  sense,  the  object  of  their  judgment  is  the 
prisoner,  and  in  another,  it  is,  let  us  say,  that  he 
is  not  guilty  of  the  offense  with  which  he  is  charged. 
There  seems,  then,  to  be  two  objects  of  judgment, 
and,  as  this  inevitably  leads  to  confusion,  Meinong 
thinks  it  important  that  they  should  be  clearly  dis- 
tinguished. For  that  purpose,  he  proposes  to  use 
the  term  'object'  to  denote  what  we  have  described 
as  the  subject-matter  of  the  judgment,  that  is,  in 
the  case  supposed,  the  prisoner;  and  the  term 
'objective*  to  denote  what  we  have  called  the  object, 
that  is,  in  the  case  supposed,  the  verdict  of  the 
judge  and  jury.  Now  Meinong  is  perfectly  right 
in  saying  that  the  object  peculiar  to  the  judgment 
is  what  he  calls  the  'objective,'  that  the  judgment 
exists  for  the  purpose  of  asserting  something  about 
a  definitely  apprehended  subject-matter,  and  he  is 
also  right  in  calling  attention  to  the  importance  of 
fixing  this  distinction  in  an  appropriate  terminology, 
because,  in  the  absence  of  such  terminology,  of  the 
tendency  to  confuse  the  two  kinds  of  objects. 

The  Universe  of  Discourse.  In  view  of  the  course 
that  our  discussion  has  taken  up  to  this  point,  the 
logical  judgment  may  be  defined  as  an  assertion  of, 
or  of  something  about,  the  objects  of  our  experience. 
We  may,  for  example,  assert  that  so  and  so  is  the 
object  of  which,  at  the  time  the  assertion  is  made, 
we  are  thinking,  or  we  may  assert  certain  other 


THE   JUDGMENT  51 

things,  besides  its  existence,  of  such  an  object.  In 
each  of  these  cases  there  is  judgment  because  the 
object  is  apprehended  as  having  a  particular  char- 
acter, of  existence  or  something  else.  The  judg- 
ment, consequently,  always  implies  a  relational 
content  of  some  sort,  that  is,  an  object  qualified  in 
a  particular  way,  and  it  is  such  relational  contents, 
as  we  have  seen,  that  it  is  the  specific  aim  of  the 
judgment  to  ascertain  and  assert.  If,  for  example, 
the  words  'dog,'  'automobile,'  'zeppelin,'  are  not  mere 
sounds,  but  significant  terms,  they  must  mean  some- 
thing more  than  they  express ;  either  that  something 
not  specified  is  'dog,'  'automobile,'  'zeppelin ;'  or  that 
the  objects  denoted  by  these  terms  exist ;  or  that  they 
have  characteristics  which  distinguish  them  from 
all  other  objects ;  or  that  they  stand  in  an  indefinite 
number  of  relations  to  each  other,  and  to  numerous 
other  objects.  Each  of  these  alternatives  illustrates 
the  peculiar  character  of  the  judgment,  since  each 
of  them  specifies  a  content  of  thought  in  which 
relations  of  some  sort  are  involved.  The  special 
object  of  the  judgment,  as  we  have  seen,  is  to 
assert  just  such  relational  contents  as  these. 

The  question  may  now  be  raised  whether  this  is 
the  whole  story  of  the  judgment,  whether,  that  is, 
the  asserted  content  embodies  the  whole  meaning 
of  an  act  of  judgment.  To  this  a  negative  reply 
must  be  given.  Such  an  answer  is  necessitated  in 
part  by  the  fact,  as  we  have  seen,  that  our  concrete 
acts  of  judgment  are  not  satisfied  with  the  assertion 
of  any  content,  but  only  with  those  that  are  ger- 


52  A   TEXT-BOOK   OF  LOGIC 

mane  to  the  motives  by  which  the  acts  of  judgment 
are  controlled.  But  the  negative  answer  is  ren- 
dered necessary  also  by  the  fact  that  the  subject 
qualified  in  the  judgment,  distinguished  as  the  log- 
ical subject,  is  only  a  part  of  the  actual  subject, 
distinguished  as  the  real  subject,  which  the  judg- 
ment, taken  as  a  whole,  is  understood  to  qualify. 
If  this  is  true,  a  judgment  asserts  only  part  of  what 
it  means,  and  we  must  understand  that  the  unas- 
serted  part  of  its  content  is  related  to  the  judgment 
as  the  judgment's  presupposition.  On  this  view, 
every  judgment  must  be  presumed  to  involve  or 
presuppose,  besides  and  as  part  of  what  it  asserts, 
a  wider  range  of  fact  in  the  light  of  which  the 
particulars  which  form  the  content  of  the  judg- 
ment's assertion  are  to  be  interpreted.  The  range 
of  fact  presupposed  by  any  of  our  judgments  is 
described  in  logic  as  a  universe  of  discourse. 

The  meaning  and  truth  of  this  statement  will  be 
readily  seen  in  a  simple  illustration.  Any  proposi- 
tion which  contains,  for  example,  the  term  'style' 
is  at  once  recognised  to  mean  one  thing  if  the  topic 
of  conversation  is  current  modes  of  dress,  and  that 
when  the  topic  of  conversation  is  literature  it  means 
something  quite  different.  Thus,  if  we  take  the  fa- 
miliar saying,  Le  style  c'est  I'homme,  in  abstraction 
from  all  contexts,  its  meaning  is  certainly  ambig- 
uous ;  and  the  only  hope  of  removing  this  ambiguity 
is  to  restore  the  saying  to  a  context  in  relation  to 
which  it  can  be  significantly  asserted.  Or,  to  borrow 
an  illustration  from  Major  in  discussing  a  closely 


THE   JUDGMENT  53 

related  topic  from  the  psychological  point  of  view, 
we  may  say  that  "if  one  is  engaged  with  astronom- 
ical matters,  the  word  'star'  means  a  heavenly  body. 
.  .  .  But  if  the  general  topic  of  our  discourse  is 
theatres  or  ball  games  or  decorations,  the  meaning 
.  .  .  of  'star'  will  likely  be  very  different."  From 
these  and  similar  illustrations  it  is  evident  that  the 
meaning  of  what  is  asserted  in  any  judgment  is 
rendered  particular  as  much  by  virtue  of  what  it 
presupposes,  that  is  by  its  universe  of  discourse,  as 
by  what  it  definitely  asserts.  We  may  say,  conse- 
quently, that  it  is  the  intention  of  every  judgment 
to  acknowledge  the  truth  of  what  it  asserts  in  the 
sphere  of  what  the  judgment  presupposes,  that  is, 
in  some  definitely  implied  universe  of  discourse. 
To  apply  this  view  to  another  case,  we  may  say  that 
the  statement,  'Mr.  Wilson  was  elected  by  the  pop- 
ular vote  of  the  people,'  asserts  a  fact  that  qualifies 
in  a  unique  way  the  political  history  of  the  United 
States,  and  not  a  fact  that  sets  Mr.  Wilson,  by 
virtue  of  his  election  to  the  presidential  office,  apart 
from  his  fellow  citizens.  Mr.  Wilson's  citizenship 
is  unaffected  by  his  election,  and,  therefore,  it  can- 
not be  in  respect  of  this  that  our  judgment  is  sig- 
nificant, but  the  election  does  determine  in  a  par- 
ticular way  the  political  history  of  the  Republic, 
and  this,  therefore,  must,  in  logical  terms,  be  the 
universe  of  discourse  within  which  our  judgment 
of  the  election  must  be  understood  to  fall. 

It  follows  from  this  view  of  the  j'udgment  that 
the  universe  of  discourse  implied  by  any  judgment 


54  A   TEXT-BOOK   OF  LOGIC 

exists  always  in  a  relatively  indeterminate  and 
incomplete  form.  This  statement  does  not  mean, 
although  it  is  sometimes  true,  that  particular  judg- 
ments indicate  only  vaguely  the  universe  within 
which  their  meaning  is  asserted.  It  means  rather 
that,  in  the  particular  which  the  judgment  asserts, 
the  universe  is  found  to  be  either  not  determined 
at  all,  or  not  to  be  determined  with  an  explicitness 
that  renders  it  serviceable  for  an  immediately  con- 
trolling purpose.  Whatever  degree  of  determinate- 
ness  the  general  field  or  subject  presupposed  by  any 
of  our  judgments  may  have,  that  field  or  subject 
can  be  used  as  a  universe  only  if  it  is  thought 
capable  of  receiving,  through  judgment,  a  more 
concrete  and  determined  form.  But  it  also  follows 
from  the  view  we  are  developing  that  judgments 
themselves  are  incomplete  and  point  beyond  them- 
selves. They  are,  as  it  were,  fragments  torn  from 
their  contexts;  but,  even  so  conceived,  they  carry 
with  them,  as  a  rule,  evidence  of  their  connection 
with  the  contexts  from  which  they  have  been  torn. 
Unless  this  were  so,  single  judgments  would  always 
remain  ambiguous.  But  if  this  were  the  case,  if, 
that  is,  there  existed  even  a  considerable  number 
of  judgments  from  which  we  are  unable  to  remove 
their  ambiguity,  because  they  do  not  point  with 
sufficient  definiteness  to  an  interpreting  context,  the 
fact  that,  apart  from  such  contexts,  they  remain 
ambiguous  is  in  itself  evidence  that  they  lack  some- 
thing which  is  characteristic  of  significant  asser- 
tions. The  meaning,  therefore,  of  any  judgment  is 


THE    JUDGMENT  55 

the  meaning  that  it  comes  to  have  by  virtue  of  its 
pointing  relevantly  to  something  which  is  not  iden- 
tical with  the  relational  content  asserted  by  it.  In 
so  far  then  as  a  judgment  has  to  be  supplemented 
by  what  its  context  supplies,  so  far  is  it  incomplete; 
and  if  this  incompleteness  is  to  be  overcome,  it  must 
be  by  what  the  judgment  enables  us  to  add  through 
its  presuppositions. 

If,  in  view  of  this  discussion,  we  now  define  the 
judgment,  more  fully  than  we  have  done  hitherto, 
as  an  assertion  of,  or  of  something  about,  the  reality 
presupposed  by  the  judgment,  we  are  immediately 
confronted  with  a  question  concerning  the  kinds  of 
reality  presupposed  by  our  various  judgments.  In 
respect  to  this  question,  it  has  been  maintained,  for 
example  by  Bradley,  that  the  real  subject  of  which 
the  thought-contents  asserted  by  all  our  judgments 
are  predicated  is  the  totality  of  really  existing  things 
which  we  call  the  universe.  Whatever  any  judg- 
ment asserts,  just  that,  so  it  is  maintained,  is  as- 
serted of  reality  in  the  sense  of  the  system  of  inter- 
related existences  known  as  the  universe.  Reality, 
according  to  this  view,  is  always  that  about  which 
we  judge,  and  our  particular  judgments  assign  to 
it,  as  its  subject,  the  concrete  details  which  such 
judgments  assert.  On  this  view,  no  question  as  to 
what  is  the  universe  presupposed  by  any  judgment 
could  arise,  or  if  it  did,  it  would  be  answered  before 
it  was  asked. 

Now,  in  considering  this  view,  we  do  not  need 
to  inquire  whether  in  the  end  we  should  be  obliged 


56  A  TEXT-BOOK   OF  LOGIC 

to  take  some  such  position  as  has  just  been  stated, 
although  there  seem  to  be  difficulties  in  the  way 
of  its  adoption;  what  rather  is  more  to  our  present 
purpose  is  to  remark  that  such  a  statement  does  not 
represent  the  actual  circumstances  in  which  many 
of  our  concrete  acts  of  judgment  are  made.  For 
instance,  the  series  of  judgments  in  which  the 
ancient  mythologies  state  the  relations  of  the  gods 
and  goddesses  to  one  another,  and  to  natural  events 
and  human  history,  cannot  be  said  to  be  made  of 
the  universe  of  really  existing  objects  in  the  sense 
that  the  series  of  judgments  which  constitute  the 
body  of  one  of  the  natural  sciences  can  be  said  to 
be  made  of  that  universe.  If,  further,  we  consider 
the  judgments  in  which  we  express  social,  ethical, 
and  aesthetical  facts  and  relations,  judgments,  as 
we  have  seen,  which  are  not  descriptive  in  the  sense 
that  scientific  judgments  are  descriptive,  but  which 
refer  human  behaviour  and  natural  phenomena  to 
a  norm  or  standard,  it  is  difficult  to  maintain  that 
these  are  made  with  immediate  reference  to  the 
universe  which  sums  up  in  itself  all  that  may  be 
called  real.  Whether  the  facts  and  relations  that 
constitute  the  subject-matter  of  mythology,  of  soci- 
ology, ethics,  and  aesthetics  can  be  asserted  of  the 
universe  of  which  the  facts  and  relations  of  the 
natural  sciences  are  asserted,  is  not  the  question 
that  confronts  us;  the  question  rather  is  whether, 
in  the  acts  of  judgment  which  give  definite  form 
to  our  knowledge  of  these  subjects,  they  are  so 
asserted,  or  whether  they  are  asserted  of  other 


THE   JUDGMENT  57 

universes  than  the  one  which  is  existentially  real. 
If  we  admit,  as  we  must,  the  latter  alternative,  if, 
that  is,  we  admit  the  existence  of  a  number  of  uni- 
verses, other  than  the  real,  within  which  judgments 
may  fall,  the  question  whether  the  real  universe 
includes  all  these,  as  is  sometimes  maintained,  is 
still  left  open,  and  we  do  not  need  to  close  it,  for 
the  reason,  if  for  no  other,  that  the  problem  involved 
belongs  to  metaphysics  rather  than  to  logic.  Logic 
is  interested  in  the  question  only  for  the  purpose  of 
emphasising  the  importance  of  ascertaining  the 
universe  in  relation  to  which,  as  a  matter  of  fact, 
particular  judgments  are  asserted  as  the  condition 
of  correctly  interpreting  such  judgments.  Thus  if 
we  were  confined  to  the  view  we  are  criticising,  the 
assertion  that  'Fishes  are  animals  which  get  their 
oxygen  from  the  water  in  which  they  live  through 
gill  slits/  and  The  Royal  dragon  of  China  has  five 
claws'  would  have  to  be  taken  as  qualifying  a  single 
universe ;  but  surely  no  one  not  blinded  by  a  theory 
could  fail  to  observe  that  in  the  former  case  we  are 
asserting  in  the  world  of  zoological  fact,  and  in  the 
latter  in  the  world  of  Chinese  heraldic  design.  The 
view,  therefore,  that  seems  most  serviceable,  and 
the  one  which  keeps  closest  to  the  facts  of  our  ordi- 
nary experience,  is  the  view  that  emphasises  the 
importance  of  bringing  particular  judgments  into 
relation  with  their  immediate  contexts  whatever 
these  may  be,  and  warns  us  against  resolving  the 
distinctions  by  which  these  contexts  are  character- 
ised into  a  single  context  about  which  the  only 


58  A  TEXT-BOOK   OF  LOGIC 

intelligible  thing  that  can  be  said  is  that,  in  some 
sense,  it  is  real  or  exists.  In  this  connection  it  may 
be  remarked  that  for  logic  the  important  question  is 
in  what  sense  the  reality  or  truth  of  an  assertion 
is  to  be  understood. 

Truth,  Probability  and  Error.  Truth,  probability 
and  error,  as  employed  in  logic,  are  terms  which 
describe  characteristics  that  belong  to  assertions, 
they  are  never  employed,  as  they  sometimes  are  in 
popular  speech,  to  designate  qualities  of  the  objects 
about  which  the  assertions  are  made.  From  the 
standpoint  of  logic,  objects  exist,  and  they  are  only 
the  assertions  which  are  made  about  particular 
existing  things  that  are  said  to  be  true,  probable, 
or  erroneous.  Truth,  probability,  and  error,  then, 
can  never  be  predicated  of  things,  but  only  of  our 
judgments  of,  or  about,  things. 

Now,  since  all  judgments  claim  to  be  true,  we 
have  to  inquire  what  we  mean  by  truth,  and  how 
there  can  be  such  things  as  probability  and  error. 
With  regard  to  the  meaning  of  truth,  it  is  pretty 
generally  agreed  that  the  notion  is  so  nearly  ulti- 
mate that  we  find  it  difficult,  if  not  impossible,  to 
offer  a  definition  which  does  not  involve  the  notion 
itself  as  one  of  the  terms.  But  if  truth  cannot  be 
defined,  we  can  describe,  in  a  more  or  less  satis- 
factory manner,  what  we  mean  when  we  use  the 
word.  We  may  say,  then,  that  an  assertion  is 
true  when  it  assigns  a  character  to  the  elements 
and  relations  of  a  subject-matter  which  are  found 
to  be  verified  when  this  subject-matter  is  investi- 


THE   JUDGMENT  59 

gated  by  appropriate  methods.  Thus  the  judgment, 
'The  fire  is  hot/  is  true,  if,  when  I  put  myself  into 
sufficiently  close  proximity  to  the  fire  referred  to, 
I  experience  the  sensation  called  heat.  Truth,  then, 
is  not  a  quality  of  judgments  merely  as  such ;  it  is 
a  quality  that  belongs  to  judgments  ad  hoc,  that  is, 
as  assertions  of  definitely  specified  contents.  When, 
in  other  words,  the  ideas  conveyed  by  a  judgment 
are  such  that,  in  the  universe  presupposed  by  the 
judgment,  there  are  facts  which  exist  in  the  manner 
it  asserts,  the  judgment  is  said  to  be  true.  Truth, 
that  is  to  say,  is  always  a  claim  that  is  set  up  on 
behalf  of  a  judgment's  object,  in  behalf,  that  is,  of 
what  Meinong  called  the  judgment's  'objective.' 

In  view  of  this  general  statement,  it  may  be 
asked  whether  any  judgment  is  true,  or  whether 
judgments  are  at  best  only  probable.  The  answer 
to  this  question  obviously  depends  upon  whether  we 
ever  need  to  go  beyond  a  judgment's  assertion  to 
ascertain  whether  the  facts  and  relations  asserted 
by  it  are  as  they  are  asserted.  When,  for  example, 
we  assert  that  The  sun  is  the  source  of  the  world's 
heat,'  it  is  obvious  that  the  verification  of  the  asser- 
tion must  be  sought  in  astronomical  physics,  that, 
in  other  words,  the  judgment  is  true  conditionally 
upon  our  being  able  to  verify,  in  the  appropriate 
universe,  the  facts  and  relations  asserted  in  the 
judgment.  But  not  all  our  judgments  are,  in  this 
sense,  assertions  about  a  given  subject;  judgments 
are  also  assertions  of  a  given  subject.  If,  for  ex- 
ample, we  say,  'The  subject  about  which  we  are 


60  A  TEXT-BOOK   OP  LOGIC 

thinking  is  the  sun  as  the  source  of  the  world's 
heat/  it  is  obvious  that,  whatever  physics  may  have 
to  say  about  this  particular  subject,  it  can  have 
nothing  to  say  that  throws  doubt  upon  the  fact  that, 
at  the  time  the  assertion  is  made,  we  are  actually 
thinking  about  this  particular  subject.  We  select 
an  illustrative  example  from  the  world  of  physical 
objects  because  arguments  for  the  absolute  contin- 
gency of  truth  have  sometimes  been  framed  on  the 
supposition  that  contingency  can  be  removed  only 
when  all  the  factors  of  the  judgment  are  merely 
states  of  one's  own  mind.  It  is  often  said,  for  instance, 
that  the  certainty  that  belongs  to  mathematics 
is  rendered  possible  by  the  fact  that  the  fundamental 
notions  of  mathematics  are  concepts  and  not  really 
existing  things.  Whether  this  view  of  mathematics 
is  correct  or  not,  it  is  certain  that  the  judgments 
which  assert  these  fundamental  notions  are  no  more 
indubitable  than  are  those  judgments  which  assert 
some  object  in  the  physical  world  as  the  object  of 
thought's  activity.  It  would  seem  to  follow,  there- 
fore, that  all  judgments  which  are  assertions  of 
particular  objects  as  the  objects  of  thought  are  true 
in  the  sense  that  it  is  not  possible  for  those  who 
entertain  them  to  be  in  any  doubt  that  those  are 
the  objects  with  which  thought  is  engaged. 

Judgments  which  make  assertions  about,  and 
are  not  merely  assertions  of,  their  subject-matter 
are  in  a  different  position  from  those  just  considered. 
The  chief  difference  is  that  in  their  case  we  have 
to  go  outside  the  judgment's  assertion  for  the  veri- 


THE   JUDGMENT  61 

fication  of  the  truth  of  what  such  judgments  assert. 
The  grounds,  that  is  to  say,  on  which  the  truth  of 
these  judgments  rest  are  to  be  found  in  the  universe 
to  which  what  the  judgment  asserts  is  known  to 
belong.  The  fact  to  which  attention  is  in  this  way 
being  directed  is  that  the  assertions  we  make  about 
the  objects  of  our  experience  do  not  derive  their 
truth  from  the  fact  that  they  are  asserted,  but  from 
the  fact  that  there  can  be  shown  to  exist  in  a  given 
universe  facts  and  relations  of  the  kind  that  our 
judgments  assert.  This  interpretation  of  the  truth 
of  our  judgments  should  not  come  as  a  surprise  to 
those  who  have  followed  the  discussions  of  this  and 
the  preceding  chapters,  for  the  demand  for  a  test 
of  truth  is  after  all  merely  a  challenge  to  refer  one's 
judgments  back  to  the  conditions  which,  in  the  first 
place,  made  them  possible.  In  this  way  we  are 
enabled  to  show  that,  when  all  the  motives  that, 
in  the  first  place,  conditioned  the  judgment  are 
operative,  the  assertion  contained  in  it  is  just  the 
assertion  that  that  situation  compels  us  to  make. 
Thus  when  the  chemist's  assertion  that  the  liquid 
contained  in  a  particular  bottle  is  sulphuric  acid  is 
called  in  question,  he  does  not  attempt  to  prove  the 
truth  of  his  judgment  by  an  emphatic  restatement 
of  it,  nor  by  any  form  or  number  of  reiterations; 
what  he  does,  if  he  wishes  to  remove  the  doubt  that 
the  question  has  raised,  is  to  apply  the  tests  for 
this  substance  which,  in  the  first  place,  convinced 
him  that  it  was  sulphuric  acid  and  not  something 
else.  We  may  conclude,  therefore,  with  reference 


62  A  TEXT-BOOK   OF  LOGIC 

to  the  class  of  judgments  under  consideration  that 
their  truth  is  conditional  upon  our  ability  to  apply 
tests  of  a  kind  suitable  to  the  character  of  the 
subject-matter  about  which  the  assertions  are  made, 
for  it  is  only  when  tested  that  we  are  able  to  com- 
pare what  is  asserted  with  what  happens  in  situ- 
ations similar  to  those  in  which  the  judgments  in 
question  originated.  In  the  absence  of  such  tests, 
judgments  of  this  class  can  only  be  said  to  have  more 
or  less  probability. 

There  are  situations,  however,  in  which  we  are 
either  unable  or  unwilling  to  verify  our  judgments, 
and  are  thus  precluded  from  determining  the  par- 
ticular degree  of  credibility  that  properly  belongs 
to  them.  In  these  cases,  the  claim  to  truth  which 
all  judgments  maintain  on  their  own  behalf  can  be 
acquiesced  in  as  little  as  it  can  be  dissented  from. 
There  belongs,  consequently,  to  the  judgments  in 
question  the  probability  that  attaches  to  any  unver- 
ified assertion  from  whatever  cause  it  may  arise. 

It  is  because  so  large  a  number  of  our  social 
judgments  are  incapable  of  the  strict  proof  that 
can  be  insisted  upon  when  the  subject  of  the  judg- 
ment is  some  part  of  the  material  universe  that, 
as  a  class,  they  have  generally  been  regarded  as 
possessing  a  lower  degree  of  certainty  than  that 
which  seems  to  belong  to  some  of  the  established 
conclusions  of  the  natural  sciences.  We  cannot 
revive  in  the  form  of  actually  existing  situations, 
for  example,  the  circumstances  which  determined 
our  actions  of  a  week  ago,  and  we  cannot,  therefore, 


THE    JUDGMENT  63 

verify  the  judgments  of  which  these  actions  are 
the  practical  expression.  That  at  the  time  indicated 
and  in  relation  to  the  situation  then  existing  we  did 
judge  so  and  so,  is  as  certain  as  any  judgment  can 
be;  but  that  the  judgment  at  which  we  then  arrived 
was  true  is,  in  the  nature  of  the  case,  beyond  the 
possibility  of  strict  proof.  It  would  certainly  be  a 
very  gratuitous  form  of  scepticism  to  repose  no 
confidence  whatever  in  any  social  judgment,  because 
all  such  judgments  labour  under  this  disadvantage; 
and  to  suggest  its  possibility  is  sufficient  to  expose 
the  absurdity  of  such  a  course.  For  it  may  be 
affirmed  that  the  disadvantage  in  question  is  not 
confined  to  the  social  judgments  we  are  now  con- 
sidering. It  may  be  urged  that  some  of  the  judg- 
ments that  are  made  about  the  material  universe 
are  incapable  of  the  experimental  proof  to  which 
our  exposition  has  pointed  as  the  test  of  truth.  Our 
belief  that  the  sum  total  of  physical  things  is  a 
universe,  is,  that  is,  a  sphere  of  material  existences 
whose  changes  are  all  subject  to  law,  is  not  beyond 
question;  and  when  the  belief  is  challenged,  as  it 
has  been  recently,  we  cannot  put  the  material  uni- 
verse itself  in  evidence  on  either  side  of  the  ques- 
tion. Such  a  belief,  and  the  judgment  in  which  the 
belief  is  asserted,  can  have  no  other  kind  of  cer- 
tainty than  that  which  belongs  to  the  social  judg- 
ments of  which  we  have  in  particular  been  speaking. 
Current  belief  undoubtedly  regards  the  moon  as  a 
sphere,  but,  on  account  of  the  particular  configura- 
tion of  the  solar  system,  it  can  never  be  a  practically 


64  A  TEXT-BOOK  OF  LOGIC 

demonstrated  fact  that  the  side  which  is  always 
turned  away  from  our  earth  is  not  flat.  Ether, 
ions,  centres  of  force,  and  atoms  themselves  are  all 
subject  to  the  same  kind  of  doubt,  whenever  any 
one,  for  what  seems  to  him  sufficient  reasons,  is 
inclined  to  call  them  in  question.  In  view  of  these 
instances,  it  is  only  fair  to  conclude  that  judgments 
about  any  sort  of  material  must  be  regarded  merely 
as  probable  whenever  we  are  unable  to  show  that 
facts  and  relations  of  the  kind  asserted  do  exist  in 
the  universe  that  is  presupposed  by  these  judgments. 
Again,  judgments  must  be  classed  as  probable 
whenever  we  are  unwilling,  for  a  reason  that  seems 
sufficient  to  us,  to  apply  the  test  of  truth.  When, 
for  example,  one  refuses  a  cup  of  coffee  of  one's 
hostess  with,  'No,  thank  you;  coffee  always  means 
a  sleepless  night/  the  judgment  by  which  we  excuse 
or  explain  our  refusal  has  no  doubt  a  certain  prob- 
ability derived  from  past  experience,  but  it  is  one 
that,  for  prudential  reasons,  we  are  unwilling  to 
verify  in  the  particular  circumstances  which  are 
the  occasion  of  its  assertion.  Sleepless  nights,  we 
may  admit,  have  followed  the  drinking  of  coffee  in 
the  past,  and  it  is  anticipated  that  a  similar  result 
will  follow  on  the  present  occasion.  In  a  case  like 
this,  which  is  typical  of  many  others  that  involve 
future  consequences  rather  than  past  acts,  we  should 
be  going  beyond  the  bounds  of  necessity  if  we  ac- 
ceded without  reservation  the  certainty  that  the 
judgment  claims  on  its  own  behalf.  We  feel,  per- 
haps, that  the  judgment  in  question  has  a  high 


THE   JUDGMENT  65 

degree  of  probability,  but  whether  it  deserves  the 
confidence,  say,  that  is  commonly  reposed  in  the 
prediction  of  a  solar  eclipse,  is  a  matter  upon  which 
it  is  not  necessary  to  dogmatise.  It  is  more  to  the 
point  to  observe  that  the  class  of  judgments  that 
we  are  discussing  is  conditional,  and,  consequently, 
that  it  is  only  if  we  suppose  the  present  situation 
is  in  all  essential  respects  similar  to  those  in  which 
the  consequence  has  followed  in  the  past,  that  we 
have  sufficient  reason  for  believing  that  a  like  con- 
sequence will  follow  on  the  present  occasion.  But 
it  is  exactly  this  supposition  of  which  the  judgment 
itself  is  unable  to  give  assurance,  and  which  there- 
fore renders  the  judgment  less, than  certain  until 
it  is  submitted  to  the  process  of  proof. 

We  may  now  pass  to  the  meaning  of  error. 
And,  in  the  first  place,  error  must  be  distinguished 
from  mere  irrelevance.  Irrelevance  may  exist  in 
either  of  two  forms.  It  may  exist,  first,  as  an  in- 
compatibility in  the  content  of  what  a  judgment 
asserts.  If,  for  example,  Shylock's  bond  had  been 
drawn  for  a  pound  of  justice,  and  not  for  a  pound 
of  flesh,  there  would  have  been  an  irrelevance  of  the 
kind  in  question,  because  the  avoirdupois  scale  can- 
not in  any  sense  be  made  the  measure  of  justice. 
The  universe  suggested  by  the  assertion,  *I  will 
have  a  pound  of  justice/  is  one  in  which  the  content, 
on  account  of  its  internal  contradiction,  cannot  pos- 
sibly get  realised.  Irrelevance  in  this  form,  then, 
arises  whenever  we  predicate  of  a  subject  qualities 
5 


66  A  TEXT-BOOK   OF  LOGIC 

and  relations  which  cannot  be  realised  in  the  uni- 
verse to  which  the  subject  is  thought  to  belong. 
Instances  of  this  occur  whenever  we  attribute  to 
purely  natural  events  moral  or  aesthetic  significance, 
or  when  we  explain  any  of  our  ideals  in  terms  of 
mechanical  causation.  Secondly,  irrelevance  may 
exist  as  an  incompatibility  between  what  is  asserted 
and  the  purpose  by  which  the  assertion  is  controlled. 
What  in  these  instances  is  asserted  may  be  true,  as, 
for  example,  'Mont  Blanc  is  snow-capped  all  the 
year  round,'  but  no  one  would  think  of  making  or 
entertaining  the  assertion  in  a  discussion  on  the 
value  of  Rotterdam  as  a  Dutch  port  of  entry  to  the 
German  Rhine.  Failure  to  understand  the  limita- 
tions that  a  guiding  purpose  or  interest  imposes  on 
what  may  and  what  may  not  be  significantly  asserted 
about  a  given  subject-matter  is  one  of  the  most 
fruitful  sources  of  confusion  in  discussions  of  all 
sorts,  and  it  is  to  this  form  of  irrelevancy  that  we 
look  for  the  origin  of  those  half-truths  which  do 
more  mischief  in  the  world  than  frank  and  un- 
blushing error.  The  comment  is  worth  while  in 
this  connection  because  it  is  to  the  avoidance  of 
such  irrelevance  that  the  student  may  look  as  one 
of  the  means  of  hastening  his  academic  and  prac- 
tical efficiency.  In  either  of  the  two  forms  which 
we  have  now  distinguished,  then,  irrelevance  is  not 
to  be  identified  with  error. 

Error,  in  contrast  with  the  second  of  the  two 
forms  of  irrelevance  just  distinguished,  is  an  asser- 
tion which  is  relevant  to  a  purpose,  and,  in  contrast 


THE    JUDGMENT  67 

to  the  first,  is  an  assertion  whose  contents  are  com- 
patible. Unless  it  possessed  both  these  marks  of  a 
true  judgment,  error  could  not  possibly  exist.  To 
emphasise  the  former  contrast,  we  may  say  that 
error  is  ascribed  to  any  judgment  which,  if  true, 
would  satisfy  the  purpose  for  which  the  judgment 
is  made.  There  follows  from  this  statement  a  con- 
sideration which  is  important  for  all  our  judgments, 
namely,  that  the  range  of  assertion  about  any 
subject-matter  is  determined  at  the  outset  by  the 
character  of  the  purpose  which  stimulates  and 
directs  the  judging  process.  In  other  words,  to 
expect  our  judgments  to  be  true  is  a  perfectly  rea- 
sonable expectation,  but  to  expect  that  they  will 
assert  the  whole  truth  is  to  convict  our  expectation 
of  being  either  unmeaning  or  false.  The  latter 
expectation  is  indefensible  for  the  same  reason  that 
the  former  is  maintained,  namely,  that  we  do  not 
as  a  rule,  nor  can  any  reason  be  advanced  why  we 
should,  encumber  our  judgments  by  asserting  non- 
significant features  of  the  subject-matter  to  which 
these  judgments  refer.  And  if  it  is  asked,  'What  is 
and  what  is  not  significant?'  we  can  only  reply  that 
that  all  depends  upon  what  the  judgment*  is  wanted 
for.  The  truth  of  this  statement  can  be  readily 
seen  in  what  occurs  when  all  interest  in  a  question 
vanishes.  In  such  a  situation  nothing  whatever 
can  get  asserted.  But  when  an  assertion  is  made, 
it  must  be  made,  not  merely  of  something,  but  for 
some  purpose,  and  it  is  the  character  of  the  purpose 
that  determines  what  feature  of  that  'something' 


68  A  TEXT-BOOK   OF  LOGIC 

is  selected  for  assertion.  There  is,  for  example,  no 
doubt  that  the  grass  is  green  and,  let  us  say,  that 
it  is  long,  but  it  is  only  the  latter  assertion  that  is 
pertinent  when  one  has  to  decide  what  instructions 
to  give  the  gardener  about  the  day's  work.  What 
one  thinks  about  any  object,  say  a  house,  depends 
upon  whether  we  are  considering  it  architecturally, 
domestically,  or  as  an  investment.  These  interests, 
no  doubt,  overlap,  but  they  are  sufficiently  distinct 
to  make  quite  irrelevant  certain  assertions  that 
might  be  made  from  one  of  these  points  of  view 
when,  as  a  matter  of  fact,  we  are  considering  it 
from  one  of  the  other  points  of  view.  But  we  do 
not  call  judgments  false  which  bear  no  relation  to 
the  interest  by  which  the  judging  process  is  initiated. 
Error  as  well  as  truth  exist  only  in  those  judgments 
which  claim  to  fulfill  the  purpose  of  the  individual 
by  whom  they  are  asserted. 

The  second  contrast  stated  above  calls  attention 
to  the  fact  that  the  contents  of  erroneous  judgments 
are,  as  we  said,  compatible.  That  is  to  say  the 
judgment  must  assign  its  content  to  a  sphere  in 
which  it  is  possible  for  that  content  to  be  realised. 
The  absence  of  incongruity  between  the  elements 
of  what  is  asserted  is  a  characteristic  of  error  as  it 
is  of  truth.  When,  for  example,  we  judge  that  an 
object  is  elliptical  when  in  reality  it  is  round,  we 
are  in  error,  but  the  error  does  not  consist  in 
assigning  it  a  shape,  but  in  attributing  to  it  the 
wrong  shape.  The  wrong  shape,  however,  is  an 
antecedently  possible  shape,  and  it  is  upon  this  ante- 


THE   JUDGMENT  6$ 

cedent  possibility  that  the  erroneous  character  of 
the  judgment  rests.  If  instead  of  asserting  that  the 
object  was  elliptical  we  had  asserted  that  it  was 
blue,  we  should  not  regard  that  as  an  error;  we 
should  regard  it  either  as  a  misunderstanding  of 
the  motive  of  the  judgment  or  as  nonsense. 

We  are  now  in  a  position  to  state  what  error  is. 
The  problem  of  error  is  greatly  simplified  when  it  is 
observed  that  no  judgment  which  fails  to  assert 
those  features  of  its  subject-matter  which  are  perti- 
nent to  the  purpose  in  hand  could  by  any  possibility 
be  regarded  as  true  or  erroneous.  They  are,  as  we 
saw,  merely  irrelevant.  It  is  only  when  judgments 
offer  themselves  as  the  means  of  satisfying  a  pur- 
pose that  they  are  ever  entertained.  There  is,  there- 
fore, from  the  standpoint  of  the  interest  involved, 
little  chance  for  error.  All  that  we  can  say  about 
a  judgment,  from  this  point  of  view,  is  that  it  does 
more  or  less  completely  fulfil  a  present  purpose.  It 
is,  therefore,  to  the  character  of  what  is  asserted 
that  we  must  look  finally  for  the  detection  of  error. 
And  here,  as  in  the  coresponding  case  of  truth,  we 
are  confronted  with  a  simple  question  of  fact.  Is 
it  a  fact,  we  must  enquire,  that  there  exist  in  the 
universe  presupposed  by  the  judgment  qualities  and 
relations  of  the  kind  asserted  in  the  judgment?  If 
there  are,  we  call  the  judgment  true;  if  there  are 
not,  we  call  the  judgment  erroneous.  Error,  then, 
may  be  defined  as  some  discrepancy  between  asser- 
tion and  fact. 


70  A  TEXT-BOOK   OF  LOGIC 

We  have  been  speaking  in  this  section  of  error 
as  a  failure  of  the  judgment  to  assert  the  significant 
qualities  and  relations  of  the  object  upon  which 
thought  is  directed.  The  term  is  also  used  to  denote 
those  mistakes  of  judgment  which  depend,  for  ex- 
ample, upon  inference.  In  this  sense  it  is  preferable 
to  speak  of  fallacies.  A  discussion  of  this  subject 
will  be  found  in  the  concluding  chapters  of  this 
book. 

REFERENCES 

H.  A.  Aikins,  The  Principles  of  Logic,  Ch.  I.,  II. 
B.  Bosanquet,  The  Essentials  of  Logic,  Lect.  II.,  III. 
J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Ch.  XXI. 
J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Part  I.,  Ch.  III. 
W.  S.  Jevons,  Lessons  in  Logic,  Lessons  VI.,  VII. 
S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  I. 

ADVANCED 

J.  M.  Baldwin,  Thought  and  Things,  Vol.  I.,  Ch.  XI.,  §§4-8; 

Vol.  II.,  Ch.  II.,  VI.,  §§  1-4. 
B.  Bosanquet,  Logic,  Book  I.,  Ch.  I. 
F.  H.  Bradley,  The  Principles  of  Logic,  Book  I.,  Ch.  I. 
W.  R.  B.  Gibson,  The  Problem  of  Logic,  Ch.  IX. 
H.  W.  B.  Joseph,  An  Introductory  Logic,  Ch.  VII. 
H.  Lotze,  Logic,  Book  I.,  Ch.  II. 
J.  S.  Mill,  A  System  of  Logic,  Book  I.,  Ch.  II. 
F.  C.  S.  Schiller,  Formal  Logic,  Ch.  VIII. 
J.  Welton,  A  Manual  of  Logic,  Vol.  I.,  Ch.  I.,  II  (ii). 

QUESTIONS 

1.  What  general  meaning  may  be  given  to  the  term  object? 

2.  In    what    several    ways    may    we    be    acquainted    with 
objects? 


THE   JUDGMENT  71 

3.  Is  the  character  of  an  object  affected  by  the  way  in 
which  it  is  apprehended? 

4.  What   do   you   understand   by  objects  being  implicated 
in  all  mental  processes? 

5.  Distinguish  three   senses   in   which   the  term   'thought' 
has  been  used,  and  state  how  they  are  related  to  each 
other. 

6.  To    which    of    the    meanings    already    distinguished    is 
thought,   from  the  logical   point  of  view,  most  closely 
related? 

7.  What  particular  aspect  of  thought  does  logic  emphasise 
in  its  use  of  the  term  judgment? 

8.  What  is  meant  by   saying  that  the   subject-matter  of 
judgment  is  the  content  of  a  thought  process?     Illus- 
trate. 

9.  Explain:    'Judgment  is  an  assertion  of  the  qualities  and 
relations  of  the  objects  of  thought.' 

10.  Is  language  necessary  to  give  thought  the  character  of 
assertion?     Explain. 

11.  State  clearly  what  you  understand  by  assertion.     Illus- 
trate. 

12.  Show  in  what  ways  judgments  are  implied,  but  not  ex- 
pressed,  in   interrogatives,   imperatives,  optatives,   and 
exclamations. 

13.  Describe  what  is  meant  by  groundless  statements,  and 
in  what  respect  do  they  differ  from  judgments? 

14.  Define  and  illustrate  the  practical   and  theoretical  as- 
pects of  thought  processes. 

15.  'Judgments    may    be    defined    as    relevant    assertions.' 
How  does  this  view  of  the  judgment  agree  with  and 
differ  from  that  stated  in  Question  9? 

16.  In  what  two  respects  may  all  judgments  be  said  to  be 
relevant? 

17.  Explain   what   is   meant   by   saying  that   judgment   is 
based  in  and  grows  out  of  our  practical  needs.     Illus- 
trate. 


72  A  TEXT-BOOK  OF  LOGIC 

18.  Define  what  you   understand  by  'practical,'   and   show 
how  unsatisfied  needs  of  the  sort  here  in  question  con- 
dition the  formation  of  judgments. 

19.  How  is  your  answer  to  the  preceding  question  affected 
by  the  fact  that  judgments  are  assertions  about  a  sub- 
ject-matter of  some  sort? 

20.  To  what  two  kinds  of  error  is  one  exposed  in  trying 
to  show  the  relation  of  thought  to  its  object? 

21.  Explain  and  illustrate  what  is  meant  by  saying  that 
the  interest  that  conditions  a  judgment  may  be  extrinsic. 

22.  What  do  you  understand  by  a  value  judgment? 

23.  Describe  the  nature  of  scientific  interest,  and  explain 
why  it  may  be  called,   in  contrast  to   other  kinds  of 
interest,  intrinsic. 

24.  Is  judgment  to  be  distinguished  from  awareness  of  an 
object?     Explain. 

25.  What  difference,  if  any,  do  you  recognise  between  the 
subject  and  the  object  of  judgment,  and  illustrate  by 
referring  to  Bradley's  distinction  between  the  'that'  and 
the  'what.' 

26.  Explain  what  Meinong  means  by  the  'object'  and  the 
'objective'  of  logical  judgments. 

27.  How  may  Meinong's  distinction  be  correlated  with  the 
view  taken  in  the  text? 

28.  'Judgment   may  be   defined   as   an   assertion   of,   or   of 
something  about,  the  objects  of  our  experience.'    Explain 
this  statement,  and  correlate  it  with  the  definitions  of 
judgment  in  Questions  9  and  15. 

29.  "Why  is  the  definition  of  judgment  given  in  the  preceding 

question  not  completely  satisfactory? 

30.  What  do  you  understand  by  a  universe  of  discourse? 
Illustrate. 

31.  Why  must  any  universe  of  discourse  have  a  more  or 
less  indeterminate  character? 

32.  Why  must  single  judgments  be  regarded  as  incomplete, 
and,  therefore,  as  being  to  some  extent  ambiguous? 

33.  How  may  this  ambiguity  be  overcome? 


THE   JUDGMENT  73 

34.  'Judgment   may  be   defined   as   an   assertion   of,   or  of 
something  about,  the  reality  presupposed  by  the  judg- 
ment/     Explain    and    compare    with    other    definitions 
given  in  Questions  9,  15,  28. 

35.  What,    according  to    Bradley,   is   the   universe   presup- 
posed by  all  our  judgments? 

36.  What  objections  can  you  urge  against  Bradley's  view? 

37.  Is  there  a  plurality  of  universes?     Justify  your  answer 
and  illustrate. 

38.  Of  what  are  truth,  probability  and  error  predicated  in 
logic? 

39.  In  what  respect  does  the  logical  differ  from  the  popular 
use  of  these  terms?     Illustrate. 

40.  What  is  the  logical  meaning  of  truth?     Illustrate. 

41.  Of  what  class  of  logical  judgments  can  you  say  that 
they  are  certainly  true?     Illustrate. 

42.  Can  the  truth  of  any  of  our  judgments  about  a  given 
subject-matter  be  maintained?     State  reasons  for  your 
answer,  and  illustrate. 

43.  What  two  conditions  compel  us  to  regard  certain  of  our 
judgments  as  probable,  not  true? 

44.  Why  do  we  generally  regard   judgments   about   social 
material  merely  as  probable? 

45.  Do  similar  reasons  apply  to  any  of  our  judgments  about 
the  material  world?     Explain  and  illustrate. 

46.  How  does  unwillingness  to  verify  an  assertion  affect  its 
claim  to  be  true? 

47.  In  what  two  forms  may  irrelevance  exist?     Explain  and 
illustrate  each. 

48.  How  do  you  distinguish  irrelevance  from  error? 

49.  Why  do  we  not  call  those  judgments  which  fail  to  fulfil 
a  purpose  erroneous?     Illustrate. 

50.  What  is  meant  by  saying  that  in  order  to  be  erroneous 
judgments  must  assert   contents   that   are  compatible? 
Illustrate. 


74  A  TEXT-BOOK   OF  LOGIC 

51.  Wherein  consists  the  nature  of  error? 

52.  Can  you  frame  a  definition  of  error? 

53.  In  what  respect  does  error  differ  from  fallacy? 

EXERCISES 

1.  In  what  sense  is  the  word,  thinking,  used  in  the  follow- 
ing statements: 

(1)  All  human  beings  are  thinking  beings. 

(2)  There  is  no  truth  or  error  but  thinking  makes  it  so. 

2.  State  at  least  two  judgments  about  each  of  the  follow- 
ing subjects: 

(1)  Mathematics  as  a  required  subject  for  college  grad- 
uation. 

(2)  Inter-collegiate  football  as  a  desirable  form  of  stu- 
dent activity. 

3.  What  are  the  grammatical  forms  of  the  following,  and 
show  in  what  sense  they  may  be  said  to  involve  judg- 
ments : 

(1)  O  wad  some  power  the  giftie  gie  us 
To  see  ourselves  as  others  see  us. 

(2)  How  oft  the  sight  of  means  to  do  ill  deeds 
Makes  deeds  ill  done. 

(3)  Can  one  desire  too  much  of  a  good  thing? 

(4)  Are  things  what  they  seem? 
Or  is  visions  about? 

(5)  Give  me  that  man 
That  is  not  passion's  slave,  and  I  will  wear  him 
in  my  heart's  core,  ay,  in  my  heart  of  hearts, 
As  I  do  thee. 

4.  Give   six   illustrations    of  what   are   called    groundless 
statements. 

5.  State  six  judgments  on  subjects  of  your  own  choosing 
that    show   the   influence   of   purpose   on    the   judging 
activity. 

6.  Give  six  illustrations  of  the  way  that  judgments  are 
controlled  by  the   nature  of  the  subject-matter   about 
which  one  thinks. 


THE   JUDGMENT  75 

7.  Take  three  instances  of  judgment  from  your  answer  to 
Question  5,  and  the  same  number  from  your  answer  to 
Question  6,  and  show  in  each  case  the  relation  of  interest 
to  subject-matter. 

8.  Take   the   remaining   instances   from   your   answers   to 
Questions  5  and  6,  and  state  what  is  the  subject  and 
the  object  in  each  case. 

9.  What  can  you  say  about  'water'  in  each  of  the  following 
universes  of  discourse:    domestic  life;  chemistry;  phys- 
ics; art;  physiology. 

10.  Examine  the  following  judgments,  and  state  whether, 
and  under  what  conditions,  you  regard  them  as  true, 
irrelevant,  probable,  or  erroneous: 

(1)  Everything  comes  if  a  man  will  only  wait. 

(2)  For  a  man's  house  is  his  castle. 

(3)  The  many  still  must  labour  for  the  one. 

(4)  Thought  is  free. 

(5)  Virtue  is  its  own  reward. 


CHAPTER  III 
THE   PROPOSITION 

Judgment  and  the  Proposition.  In  text-books  of 
logic,  it  is  usual  to  discuss  the  judgment  and  the 
proposition  in  the  same  chapter,  and  to  emphasise 
the  points  of  similarity  between  them.  In  the  pres- 
ent chapter,  we  are  to  consider  the  proposition  by 
itself,  because  in  this  way  we  shall  be  able  not  only 
to  distinguish  between  it  and  the  judgment,  but  to 
group  together  certain  problems  that  arise  out  of 
the  nature  of  the  proposition  which  are  more  or  less 
distinct  from  those  of  the  judgment  which  were  dis- 
cussed in  the  previous  chapter. 

In  its  most  general  meaning,  a  proposition  may 
be  defined  as  the  verbal  expression  of  a  judgment. 
As  we  proceed,  this  statement  will  be  made  more 
explicit;  but  it  will  suffice  for  our  present  purpose 
if  it  enables  us  to  understand  the  importance  of  put- 
ting into  verbal  form  the  truths  that  are  asserted 
in  our  judgments.  The  necessity  of  finding  a  suit- 
able medium  for  expressing  our  judgments  is  forced 
upon  us  when  it  is  realised  that  explicit  statements 
of  our  meanings  are,  sometimes,  if  not  frequently, 
important  factors  in  our  search  for  truth.  We  often 
find,  for  example,  that  ideas  with  which  we  had  sup- 
posed ourselves  perfectly  familiar  suddenly  take  on 
a  penumbral  haze  when  we  are  required  to  use  these 
ideas  in  working  out  new  problems,  —  for  instance, 

(76) 


THE   PROPOSITION  77 

in  solving  an  'original'  in  geometry  or  in  finding  an 
'unknown'  in  chemistry ;  or  when  we  try  to  commu- 
nicate these  ideas  to  other  people,  —  for  instance, 
in  a  class  recitation.  In  both  these  cases,  we  have 
before  us  the  task  of  setting  the  ideas  in  question 
in  a  different  context,  and  it  is  the  new  context  into 
which  they  are  to  be  fitted  that  reveals  to  us  defects 
in  the  ideas  themselves  of  which  we  were  hitherto 
unaware.  In  order  to  succeed  in  the  problem  that 
is  thus  presented,  it  often  becomes  necessary  to  give 
verbal  expression  to  our  ideas,  and  our  search  for 
the  suitable  form  is  not  infrequently  found  to  re- 
act upon  the  ideas  themselves  to  make  them  more 
exact.  It  may  also  be  noticed  that  when  we  have 
once  expressed  our  ideas  in  accurate  verbal  forms, 
we  are  able  to  analyse  these  ideas,  and  thus  to  ad- 
just them  to  other  ideas  with  which  they  have 
various  relations.  For  it  must  be  admitted  that  our 
interest  in  ideas  is  not  merely  to  know  that  they  are 
true,  but,  concurrently  with  this,  to  use  them  in  en- 
larging the  boundaries  and  directions  of  our  knowl- 
edge. And  it  contributes  to  both  these  objects  to 
secure  for  our  ideas  an  adequate  verbal  expression. 
The  statement  of  our  judgments  in  the  form  of  prop- 
ositions both  clarifies  the  meaning  and  renders  the 
application  of  our  ideas  possible. 

We  may  bring  out  the  difference  between  the 
judgment  and  the  proposition  if  we  refer  to  the  way 
that  each  originates  in  our  ordinary  experience.  In 
the  foregoing  chapter,  we  have  had  occasion  to  indi- 
cate in  a  general  way  the  conditions  under  which  our 


78  A   TEXT-BOOK   OF  LOGIC 

judgments  arise.  Judgments  were  there  described 
as  completed  solutions  of  problems  set  by  the  situ- 
ations in  which  one  finds  himself  from  time  to  time. 
That  is  to  say,  judgments  arise  out  of  whatever  is 
problematical,  undetermined,  baffling,  whether  this 
falls  in  the  sphere  of  perception,  or  in  the  sphere 
of  the  social,  scientific,  ethical,  sesthetical,  or  relig- 
ious life.  Whatever  sets  a  barrier  to  the  satisfac- 
tion of  wishes,  whatever  hinders,  arrests,  or  makes 
impossible  the  carrying  out  of  cherished  plans,  chal- 
lenges and  stimulates  the  life  of  thought,  and  forces 
us  into  a  judgment.  Judgments  arise  out  of  our 
needs  for  knowledge,  and  this  need  is  stimulated 
when  the  situation  which  instigates  the  need  is  of 
such  a  character  that  our  way  to  the  successful  con- 
duct of  the  theoretical  or  practical  life  is  blocked. 
When  we  have  unravelled  the  tangle,  and  see  the 
total  situation  in  its  bearing  upon  our  arrested  pur- 
suits so  that  we  either  modify  or  change  our  aims,  or 
they  are  given  an  open  field,  we  may  be  said  to  have 
judged.  It  is  another  story  when  we  ask  what  are 
the  conditions  that  determine  the  rise  of  proposi- 
tions. In  the  proposition  we  are  not  seeking  to 
extricate  ourselves  from  an  embarrassment,  because 
no  embarrassment  is  present,  and  we  are  not  seeking 
knowledge,  because  that  already  exists.  A  proposi- 
tion, as  we  have  already  said,  is  the  verbal  statement 
of  what  we  already  know ;  it  is  a  statement  in  which 
something  is  either  affirmed  or  denied  of  something 
else.  It  is,  consequently,  not  an  instrument  of  the 
search  for  knowledge,  but  of  its  communication. 


THE   PROPOSITION  79 

When  we  put  our  judgments  into  propositional  form, 
we  are  making  them  socially  available,  and  present- 
ing them  for  acceptance  or  rejection. 

The  Import  of  Propositions.  A  proposition  may 
be  interpreted  from  either  or  both  of  two  points  of 
view :  from  the  point  of  view  of  the  person  speaking, 
and  from  the  point  of  view  of  the  person  spoken  to. 
In  each  of  these  cases,  the  proposition  has  a  different 
import  or  meaning.  In  the  former,  where  the  person 
speaking  is  expressing  a  judgment  concerning  a  sub- 
ject about  which  he  has  reached  a  conclusion,  the 
proposition  means  what  the  judgment  which  it  ex- 
presses means,  and  must  be  interpreted  as  a  judg- 
ment. That  is  to  say,  the  truth  of  the  proposition 
is  also  the  truth  of  its  corresponding  judgment,  and 
vice  versa.  The  meaning  of  the  proposition,  inter- 
preted from  the  point  of  view  of  the  speaker,  is 
designated  in  logic  as  the  truth-import  of  the  propo- 
sition. In  the  other  case,  when  we  consider  the 
proposition  from  the  standpoint  of  the  hearer  of  it, 
the  proposition  and  the  judgment  which  it  expresses 
are  not  the  same,  and  the  truth  they  express  may  not 
be  identical.  The  reason  why  the  proposition  may 
mean  one  thing  to  the  hearer  and  another  to  the 
speaker  must  be  looked  for  in  the  differences  of  the 
relations  that  the  hearer  and  speaker  have  to  the 
knowledge  that  the  proposition  embodies.  Or,  to 
put  the  matter  more  definitely,  the  speaker's  rela- 
tions are  with  the  knowledge  which  the  proposition 
expresses,  while  the  hearer's  are  with  the  terms  of 
the  proposition  itself.  When  we  interpret  a  propo- 


80  A  TEXT-BOOK   OF  LOGIC 

sition  from  the  standpoint  of  the  person  spoken  to, 
we  have  what  is  called  in  logic  the  statement-import 
of  the  proposition.  The  statement-import  is,  conse- 
quently, a  structural  interpretation  of  the  proposi- 
tion ;  it  is  the  meaning  that  a  proposition  has  when 
it  is  considered  from  the  standpoint  of  its  factors 
or  terms. 

We  may  look  at  this  distinction  between  the 
statement-import  and  the  truth-import  of  proposi- 
tions a  little  more  in  detail.  It  is  obvious  that  the 
question  before  the  speaker  is  one  of  selecting  the 
words  that  will  adequately  convey  his  meaning. 
When  one  wishes  to  make  a  judgment  socially  avail- 
able, one  has  to  express  the  judgment  in  words,  or  in 
some  other  recognised  means  of  communication. 
When,  on  the  other  hand,  we  listen  to  what  is  said, 
or  read  what  is  written,  the  question  before  us  is  to 
ascertain  the  meaning  that  the  words  were  originally 
intended  to  convey.  This  is  not  always  as  simple  as 
it  may  sometimes  seem.  Because,  for  example,  the 
words  in  which  we  are  addressed  are  familiar,  it  does 
not  follow  that  the  idea  that  the  words  express  is  at 
all  understood.  The  common  misunderstandings  of 
ordinary  life,  and  the  more  serious  difficulties  that 
we  meet  with  in  the  course  of  our  studies,  are  due 
very  often  to  our  failure  to  interpret  aright  the 
meaning,  not  to  our  inability  to  understand  the 
words,  of  the  propositions  that  are  laid  before  us. 
In  such  a  case,  the  proposition  means  for  us  some- 
thing that  it  does  not  mean  for  the  speaker;  it  has 


THE   PROPOSITION  81 

for  us,  that  is  to  say,  a  statement-import  but  no 
truth-import. 

It  will  help  our  understanding  of  this  statement 
if  we  throw  the  essential  factors  of  our  problem  into 
the  form  of  a  diagram : 

Speaker  Hearer 


f  \        f  > 

Idea —  — ••  Proposition —  — *  Idea 

V  J        V, J 

^Y"  ~~Y~~" 

Truth-import  Statement-import 

If,  reading  the  above  diagram,  our  interpretation  of 
the  proposition  is  made  from  the  standpoint  of  the 
speaker,  we  start  with  the  idea  or  judgment  that  has 
to  be  expressed  in  the  proposition;  the  proposition 
is  then  the  verbal  expression  of  the  judgment  or 
idea  from  which  we  set  out.  For  the  speaker,  the 
proposition  does  express  his  judgment,  and  so  inter- 
preted it  embodies  the  truth  of  his  judgment.  If, 
on  the  other  hand,  our  interpretation  is  made  from 
the  standpoint  of  the  hearer,  we  start  with  the  prop- 
osition, the  verbal  expression  of  the  speaker's  judg- 
ment, and  the  words  of  the  proposition  have  to  be 
interpreted  so  as  to  render  an  idea  or  judgment  pos- 
sible. But  what  is  the  guarantee  in  such  a  case  that 
the  meaning  derived  from  the  proposition  will  be 
the  meaning  expressed  by  it?  The  idea  in  the 
hearer's  mind  may  be  different  from  the  idea  in  the 
speaker's  mind.  It  is  this  idea,  the  idea  or  meaning 
that  the  hearer  of  a  statement  gets  from  what  is  said 


82  A   TEXT-BOOK   OF  LOGIC 

to  him,  that  we  designate  the  statement-import  of 
the  proposition.  The  truth-import  and  the  state- 
ment-import of  a  proposition,  therefore,  may  not  be 
the  same. 

But,  it  may  be  asked,  does  not  our  interpretation 
of  a  proposition,  even  when  it  is  taken  from  the 
standpoint  of  the  hearer,  aim  at  an  identity  of  mean- 
ing between  its  truth-import  and  the  statement- 
import?  This  is  doubtless  true.  But  we  should 
miss  a  great  deal  in  our  understanding  of  the  life  of 
thought  if  we  did  not  see  the  possibility  of  the  same 
statement  meaning  different  things  for  speaker  and 
hearer.  It  is  this  fact  that  we  have  been  emphasis- 
ing. And  it  is  as  desirable  to  ascertain  how  this 
difference  may  arise  as  to  see  how  it  may  be  over- 
come. For  if  we  understand  the  origin  of  such  dif- 
ferences, we  shall  know  how  to  avoid  or  overcome 
them.  In  either  case,  we  are  concerned  with  the 
context  of  the  idea  or  judgment  that  we  are  trying 
to  understand ;  and  it  is  obvious  that  when  the  con- 
text is  different  for  speaker  and  hearer,  the  idea 
the  proposition  conveys  must,  in  some  measure,  be 
different  for  both.  For,  as  we  have  seen,  the  con- 
texts in  which  our  ideas  occur  give  part  of  the  mean- 
ing that  ideas  may  have.  If,  therefore,  you  change 
the  contexts  you  change  also  in  part  the  ideas  them- 
selves. Thus,  whenever  we  fail  to  get  the  meaning 
of  what  is  said  to  us  by  reason  of  our  failure  to 
understand  the  universe  of  discourse  within  which 
the  thought  of  the  speaker  is  moving,  we  do  not 
naturally  ask  for  a  repetition  of  the  sentence  or 


THE   PROPOSITION  83 

proposition,  but  require,  for  its  comprehension,  a 
larger  section  of  the  context,  and,  in  some  cases,  the 
revival  of  the  whole  universe  within  which  the  truth 
of  the  judgment  is,  by  the  speaker,  presumed  to 
exist.  In  other  words,  it  is  the  fragmentariness  of 
all  our  judgments,  to  which  reference  has  been  made, 
that  is  the  ground  of  the  difference  between  the 
truth-import  and  the  statement-import  of  proposi- 
tions ;  a  fragmentariness  that  can  be  overcome  only 
if  it  is  supplemented  by  a  larger  portion  of  the  inter- 
preting context  than  is  frequently  implied  by  the 
single  proposition. 

We  may  further  elucidate  the  important  distinc- 
tion just  made  between  the  truth-import  and  the 
statement-import  of  propositions  if  we  consider  it 
as  a  special  instance  of  the  difference,  first  drawn 
by  the  English  historian,  Grote,  and  made  current 
by  the  American  psychologist,  James,  between 
"knowledge  of  acquaintance"  and  "knowledge 
about."  An  illustration  sometimes  used  to  indicate 
the  contrast  between  these  two  kinds  of  knowledge 
is  the  difference  between  the  normal  child's  expe- 
rience of  light,  and  the  experience  of  light  that  a 
child,  blind  from  birth,  has  through  the  reports  of 
seeing  adults.  The  knowledge  of  the  two  children, 
without  doubt,  is  at  different  removes  from  the  real 
character  of  light.  That  is  to  say,  the  contrast  be- 
tween "knowledge  of  acquaintance"  and  "knowledge 
about"  calls  attention  to  the  fact  that  the  knowledge 
that  any  one  has  is  sometimes  immediate  and  direct, 
and  sometimes  mediate  and  indirect.  Now,  the  dis- 


84  A  TEXT-BOOK   OF  LOGIC 

tinction  between  the  truth-import  and  the  statement- 
import  of  propositions  seems  to  be  contingent  upon 
whether  propositions  express  either  the  one  or  the 
other  of  the  above-mentioned  kinds  of  knowledge. 
We  are  all  aware  that  much  that  we  ordinarily  call 
knowledge  is  based  upon  nothing  more  certain  than 
our  ability  to  understand  the  words  in  which  this 
knowledge  has  been  communicated,  while  a  much 
smaller  fraction  of  our  knowledge  rests  on  direct 
acquaintance  with  the  facts,  and  a  study  of  the  rea- 
sons by  which  such  knowledge  is  supported.  In  the 
one  case,  propositions  embody  judgments,  and  are 
to  be  interpreted  as  judgments;  in  the  other  case, 
propositions  are  statements  to  be  understood, 
whether  they  introduce  us  or  not  to  the  facts  out  of 
which  the  judgments  which  they  express  have  come. 
To  understand  what  is  told  us  is  a  first  step  in  knowl- 
edge; but  it  is  only  a  first  step,  and  should  lead  us 
beyond  itself  to  a  more  intimate  and  personal  ac- 
quaintance with  the  truths  and  facts  that  are  the 
material  of  advancing  knowledge.  In  other  words, 
we  must  proceed  from  the  statement-import  to  the 
truth-import  of  the  propositions  which  convey  to  us 
so  large  a  proportion  of  the  material  upon  which  the 
educative  processes  as  a  whole  depend. 

Formal  Analysis  of  the  Proposition.  The  propo- 
sition was  defined  above  as  the  verbal  expression  of 
a  judgment;  it  is  the  logical  instrument  by  which 
what  is  true  for  judgment  gets  a  simple  and  un- 
equivocal expression.  But  not  every  verbal  expres- 
sion of  a  judgment  is  a  proposition;  it  may  be,  for 


THE   PROPOSITION  85 

example,  a  sentence.  A  sentence  may  be  a  proposi- 
tion, as,  for  example,  'The  book  is  on  the  table ;'  but 
this  is  not  necessarily  the  case,  as,  for  example,  'A 
friend  of  mine  has  gone  abroad/  From  the  formal 
side,  the  essential  difference  between  the  sentence 
and  the  proposition  lies  in  the  number  of  the  factors 
present  in  each.  A  sentence  always  requires  the 
presence  of  a  subject  and  a  predicate;  the  proposi- 
tion cannot  exist  without  a  subject  and  predicate, 
which  are  called  terms,  and  also  a  copula.  If  we 
compare  the  sentence  and  the  proposition  in  these 
respects,  we  shall  see  that  the  predicate  of  the  sen- 
tence is,  by  logic,  broken  up  into  two  parts,  the 
copula  and  the  predicate  of  the  proposition,  and  that 
the  subject  remains  the  same.  The  following  dia- 
gram represents  these  relations  to  the  eye : 

Sentence:          Subject  Predicate 

A 


Proposition:     Subject     Copula  Predicate 

The  doctrine  of  formal  logic  depends  upon  the  struc- 
tural difference  between  the  proposition  and  the  sen- 
tence as  thus  outlined.  In  the  following  sections, 
therefore,  we  shall  dwell  on  the  meaning  that  logic 
assigns  to  the  several  parts  of  the  proposition. 

Terms.  The  subjects  and  predicates  of  proposi- 
tions are  called  terms.  Now,  since  the  proposition 
is  a  statement  in  which,  as  we  have  seen,  something 
is  predicated  —  affirmed  or  denied  —  of  something 
else,  we  may  define  the  predicate  term  as  that  which 
is  predicated,  and  the  subject  term  as  that  of  which 


86  A  TEXT-BOOK   OF  LOGIC 

the  predication  is  made.  If,  as  is  usual,  we  use  the 
symbol  S  for  the  subject  term,  and  the  symbol  P 
for  the  predicate  term,  the  structural  proposition 
may  be  written  S — P.  In  such  a  proposition,  P  is 
said  to  be  predicated  of  S.  We  may  observe  that 
the  subject  term  of  a  proposition  is  always  written 
first,  and  the  predicate  term  last.  The  reason  for 
this  seems  to  be  that  since  the  proposition  is  deter- 
mined by  the  interests  of  communication,  it  is  im- 
portant, at  first,  to  call  attention  to  that  about  which 
we  wish  to  speak.  If  the  student  remembers  this 
he  will  avoid  the  difficulty  that  is  sometimes  expe- 
rienced in  distinguishing  between  S  and  P.  For 
example,  if  we  wished  to  express  in  prepositional 
form  the  statement,  'Uneasy  lies  the  head  that  wears 
a  crown,'  it  would  not  be  accurate  to  say  that  'Un- 
easy' is  the  subject.  The  rule  that  may  be  followed, 
whenever  we  are  in  doubt  as  to  what  our  terms  are, 
is  to  ask:  What  am  I  speaking  about?  The  answer 
to  this  question  will  give  us  the  subject  term.  The 
predicate  term  may  be  found  by  asking,  What  am 
I  saying  of  this?  If  we  apply  these  tests  to  the 
example  just  cited,  we  shall  find  that  we  are  speak- 
ing about  'The  head  that  wears  a  crown/  and  this, 
consequently,  is  the  subject  term  of  the  proposition ; 
and  that  what  we  are  saying  of  this  is  that  it  is 
'uneasy,'  and  this,  consequently,  is  the  predicate  of 
the  same  proposition. 

It  should  be  remarked  that  we  are  frequently 
at  a  loss  to  know  which  is  the  subject,  and  which 
the  predicate,  term  of  given  statements.  The  reason 


THE    PROPOSITION  87 

for  this  seems  to  be  that  in  order  to  know  what  any 
statement  means  we  require  sometimes  to  have  be- 
fore us  a  larger  section  of  the  whole  context  of 
thought  than  the  particular  statement  itself  pro- 
vides. This  takes  us  back  to  what  we  said  above 
about  'the  universe  of  discourse/  and  the  function 
it  serves  in  giving  to  our  particular  judgments  the 
meaning  they  are  intended  to  have.  Propositions 
express  judgments  which  are  torn  loose  from  their 
contexts,  and  they  sometimes  do,  and  sometimes  do 
not,  retain  sufficient  of  the  original  context  to  make 
our  interpretation  of  them  certain.  The  example 
that  was  quoted  above  illustrates  the  former  case; 
we  were  doubtless  talking  about  'crowned  heads.' 
A  more  difficult  case,  taken  from  Jevons,  is  the  fol- 
lowing: 'Life  is  held  dear  by  every  man.'  In  this 
statement,  are  we  talking  about  'life,'  or  about 
'things  that  are  held  dear,'  or  about  'every  man'? 
Grammatically,  'life'  is  the  object  of  the  verb  'holds 
dear,'  and  cannot,  therefore,  be  the  subject.  The 
meaning  of  the  statement,  consequently,  is :  'Every 
man  holds  life  dear.'  We  are  speaking  in  the  uni- 
verse of  values ;  and,  in  the  statement,  we  are  nam- 
ing one  of  the  objects  of  value.  If,  however,  to  take 
an  illustration  from  Sidgwick,  we  say  that  'Newman 
wrote  the  Grammar  of  Assent,'  we  have  no  means 
of  determining  whether  'Newman'  or  The  Gram- 
mar of  Assent'  is  the  subject,  because,  as  Sidgwick 
says,  "the  statement  is  regarded  in  isolation  from 
all  context.  Regarded  in  this  abstract  way,  it  may 
equally  well  be  called  a  statement  about  Newman, 


88  A  TEXT-BOOK   OF  LOGIC 

or  about  the  book,  or  again  about  both  the  man  and 
the  book."  It  would  seem,  then,  that  back  of  all 
particular  statements  there  lies  a  universe  of  fact 
or  idea  which  flows  over  into  these  statements  to 
give  them  the  determinate  meaning  they  may  prop- 
erly have. 

Names  and  Words.  Another  question,  closely 
connected  with  the  foregoing,  arises  when  we  ask 
whether  terms  can  exist  outside  the  propositions  in 
which  they  are  found.  We  may  ask,  for  example, 
whether  The  head  that  wears  a  crown/  which,  as  we 
saw,  was  the  subject  term  of  the  proposition  which 
was  studied  above,  is  always  a  term,  and  in  what- 
ever connection  we  may  meet  the  phrase.  Or,  we 
may  inquire,  is  it  a  term  only  when  it  occurs  in  a 
proposition?  To  this  question  we  reply  that  terms 
are  terms  only  in  relation  to  the  proposition  in 
which  they  occur.  For  example,  we  may  write 
down  the  following : 

Silver  Conductor  of  electricity    Comets 

Plants  Without  weight  Roses 

But  neither  this,  nor  any  similar  list,  is  a  list  of 
terms.  In  logical  terminology,  this  is  a  list  of 
Names.  By  a  name,  therefore,  we  understand  a 
word,  or  a  collection  of  words,  which  has  a  complete 
meaning,  and  which  may  be  used  as  the  subject  or 
predicate  of  a  proposition.  In  the  following,  'Silver/ 
'Without  weight/  'Plants/  etc.,  names  from  the 
above  list,  are  terms : 


THE   PROPOSITION  89 

Silver  is  a  conductor  of  electricity. 
Comets  are  without  weight. 
Roses  are  plants. 

Now  it  may  seem  that  the  distinction  between 
terms  and  names  is  over-drawn,  and  that  it  does  not 
correspond  to  any  real  difference.  This  is  not  the 
case.  For  observe  that  although  the  words  in  the 
list  of  names,  and  the  words  that  appear  in  the 
propositions  are  the  same,  the  meaning  in  the  latter 
case  is  much  more  precise  than  in  the  former;  it 
has  changed  from  being  vague,  general,  and  loose, 
to  being  specific,  particular,  and  fixed.  In  so  far  as 
our  propositions  express  judgments,  this  is  the  re- 
sult that  we  should  expect  to  find.  For  the  sake 
of  emphasis,  the  difference  between  a  name  and  a 
term  may  be  stated  in  the  following  way: 

A  Name  is  a  word,  or  a  collection  of  words,  with 
a  complete  meaning,  which  may  be  thought  of  as 
the  S  or  P  of  a  proposition. 

A  Term  is  a  word,  or  collection  of  words,  with 
a  complete  meaning,  which  is  thought  of  as  the  S 
or  P  of  a  proposition. 

Both  terms  and  names  are  ordinarily  expressed 
in  words,  but  it  is  not  because  they  are  words,  but 
because  they  have  meaning  that  they  are  so  called. 
Terms  and  names  are  significant  words.  We  are 
not  confined,  however,  to  the  study  of  words  from 
the  standpoint  of  their  significance  or  meaning. 
Grammar,  for  example,  studies  words  with  respect 
to  the  uses  they  have  in  sentences.  Substantitives, 


90  A  TEXT-BOOK   OF  LOGIC 

verbs,  prepositions,  adjectives,  adverbs,  etc.,  are  the 
names  of  various  classes  of  words  that  are  recog- 
nised by  grammar  when  their  use  is  made  the  basis 
of  classification.  Logic  also  finds  it  convenient  to 
classify  words  with  respect  to  their  uses  as  terms 
in  the  proposition,  disregarding,  as  does  grammar, 
the  meaning  that  particular  words  may  have.  But 
the  logical  classification  is  simpler  than  the  gram- 
matical, because  the  logical  requirements  are  nar- 
rower and  more  precise  than  the  grammatical. 
Words,  for  logic,  are  arranged  in  two  main  groups, 
according  as  they  are  or  are  not  able  to  stand  by 
themselves  as  S  or  P  in  a  proposition.  Words  which 
by  themselves  are  capable  of  being  thought  of  as  S 
or  P  of  a  proposition  are  called  Categorematic 
words.  Words,  on  the  other  hand,  which  require  the 
assistance  of  other  words  before  they  can  be 
thought  of  as  the  S  or  P  of  a  proposition  are  called 
Syncategorematic  words.  'Metal/  'laws/  'elements/ 
'custom/  are  categorematic  words,  since  they  may 
stand  by  themselves  as  terms  in  a  proposition.  For 
example : 

All  metals  are  elements. 
Some  laws  arise  from  custom. 

The  words  'of/  'the/  'always/  'a/  in  the  following 
statements,  are  syncategorematic  words,  because  by 
themselves  they  cannot  be  thought  as  S  or  P  in  a 
proposition. 


THE   PROPOSITION  91 

Mistakes  are  not  always  a  proof  of  ignorance. 
Bismarck  is  the  man  of  iron. 
A  burnt  child  dreads  the  fire. 

The  only  apparent  exception  to  the  statement  of 
what  should  be  understood  by  a  syncategorematic 
word  is  illustrated  by  such  instances  as  the  follow- 
ing: 'Good  is  an  adjective,'  'Of  is  a  preposition/ 
But  it  should  be  observed  that  it  is  not  the  use  of 
the  word  in  a  logical  proposition,  but  the  word  as 
an  example  of  a  group  of  words  in  grammar  that 
is  the  subject  term  of  such  propositions.  They  are 
for  logic  categorematic  words. 

If  we  examine  the  logical  classification  of  words, 
we  shall  see  that  the  terms  of  propositions  in  which 
categorematic  words  occur  are  single-worded  terms, 
while  the  terms  of  propositions  in  which  syncatego- 
rematic  words  occur  must  necessarily  be  many- 
worded  terms.  On  the  basis,  therefore,  of  the 
kinds  of  words  that  enter  into  them,  we  may 
classify  terms  as  either  single-worded  or  many- 
worded  terms. 

The  Copula.  The  most  distinctive  element  of  the 
proposition  is  the  copula.  It  is  always  expressed 
by  'is'  or  'is  not,'  'are'  or  'are  not,'  depending  on 
whether  the  subject  term  of  the  proposition  is  sin- 
gular or  plural,  and  whether  the  judgment  is  affirm- 
ative or  negative.  From  the  standpoint  of  the 
hearer,  the  proposition  tends  to  fall  apart  into  its 
terms;  and  it  is  the  function  of  the  copula  to  hold 
them  together  in  the  concrete  unity  of  a  single  idea, 


92  A  TEXT-BOOK   OF  LOGIC 

and  thus  .to  preserve  in  the  proposition  a  quality 
that  is  characteristic  of  the  judgment  itself.  The 
copula  must  not  be  looked  upon  as  a  coupler  be- 
tween the  subject  and  predicate  terms,  nor  is  there 
any  separate  and  distinct  element  in  the  judgment 
corresponding  to  it,  and  coming  between  the  idea  of 
the  subject  and  that  of  the  predicate.  Its  function 
is  to  express  the  act  of  judgment  by  which  the  S 
and  P  are  really  held  together  in  the  way  that  the 
proposition  expresses. 

The  copula  has  been  a  much  debated  subject  of 
logic.  It  will  help  us  to  a  better  understanding  of 
it  if  we  consider  some  of  the  views  that  have  been 
advanced  concerning  it.  We  may  distinguish  two 
such  views,  the  relational  and  the  existential,  and 
these  we  shall  touch  upon  briefly  in  order. 

The  Relational  View.  This  view  is  based  upon 
the  assumption  that  each  term  of  the  proposition 
has  a  distinct  meaning,  and  it  holds  that  the  copula 
brings  these  terms  together  in  the  unity  of  a  single 
statement.  If  we  -adopt  this  view,  we  are  required 
to  admit  that  our  concepts  or  terms  are  independent 
of  our  judgments,  and  .that  is -to  deny  that  judgment 
is  the  starting-point  of  knowledge.  The  discussions 
of  the  logicians  of  the  Middle  Ages  over  Univer- 
sals  were  concerned  with  this  subject,  and  they  were 
divided  in  their  opinion  as  to  whether  concepts  ex- 
isted apart  from  our  knowledge  of  them.  The  views 
developed  by  the  Schoolmen,  as  the  great  thinkers 
of  the  Middle  Ages  were  called,  are  three,  and  these 
wei  may  enumerate  and  describe  briefly.  The  real- 


THE   PROPOSITION  93 

istic  view,  held  by  Anselm  and  Aquinas r  was  that 
universals  or  concepts  have  an  existence  before  and 
independently  of  the  particular  objects  through 
which  we  become  aware  of  them.  Briefly  expressed, 
this  position  was  summarised  in  the  Latin  state- 
ment: Universalia  ante  rem.  The  view  of  the 
Nominalists  was  that  universals  or  concepts  owe 
their  existence  to  the  prior  existence  of  the  par- 
ticular objects  of  our  experience,  or,  as  they  said, 
Universalia  post  rem.  This  view  was  held,  among 
others,  by  Roscellinus.  A  conceptualist  view, 
which  aimed  to  embody  the  truth  of  each  of  the  for- 
mer views,  was  developed  by  Abelard.  This  view 
called  attention  to  the  fact  that  universals  or  con- 
cepts have  no  meaning  apart  from  the  particular 
objects  in  which  they  are  embodied,  and  that  par- 
ticular objects  have  no  meaning  apart  from  the  uni- 
versal or  concept  which  gives  them  their  significance. 
These  ideas  are  expressed  in  the  Latin  statement: 
Universalia  in  re.  Outside  the  official  teaching  of 
the  Roman  Church,  which  is  realistic,  some  form  of 
conceptualism  quite  generally  prevails  at  the  present 
day.  At  any  rate,  it  would  be  agreed  by  most  logi- 
cians that  concepts  are  elements  of  our  knowledge, 
and  that  it  is  our  ability  to  judge,  —  to  assert  like- 
nesses and  differences  of  the  objects  of  our  expe- 
rience, —  that  gives  existence  and  life  to  the  things 
we  call  concepts.  Psychology  and  logic  both  teach 
that  the  objects  of  our  experience  are  inextricably 
connected,  and  that  our  knowledge  grows  by  dis- 
tinguishing now  one  aspect  and  now  another  of  the 


94  A  TEXT-BOOK   OF  LOGIC 

inter-related  world  of  men  and  things  around  us. 
If  this  is  true,  there  is  no  object  that  is  merely 
itself,  or  that  exists  in  isolation  from  everything 
else.  Every  object  with  which  we  are  in  any  way 
concerned  is  always  becoming  for  us  something  else, 
showing  some  new  quality  or  entering  into  some 
new  relation.  This  state  of  affairs  is  expressed  in 
logic  by  saying  that  there  are  no  S's  that  are  not  P's, 
that  the  P  predicated  of  any  S  is  not  a  foreign  thing 
that  is  added  to  it  by  the  copula,  but  some  quality 
that  it  already  possesses,  or  some  relation  that  it 
actually  sustains.  In  other  words,  we  never  start 
with  a  bare  S,  with  an  S  that  is  an  unrelated  unit, 
but  with  an  SP  that  is  a  relational  unity,  and  it  is 
this  fact  that  becomes  explicit  in  the  judgment,  S 
is  P.  Unless  S  were  already  P,  judgment  would  be 
impossible,  and  the  proposition  could  not  exist.  The 
proposition  makes  explicit  what  is  already  present 
in  knowledge,  and  since  knowledge,  whatever  its 
form,  is  a  qualification  of  an  S  by  a  P,  there  does 
not  seem  to  be  any  separate  meaning  for  the  copula 
when  knowledge  is  expressed  in  a  proposition.  That 
is  to  say,  we  do  not  need  the  copula  for  the  estab- 
lishment of  the  knowledge  relation;  but  it  is  used 
in  the  proposition,  as  Mill  asserts,  as  "a  sign  of 
predication."  In  other  words,  the  copula  must  be 
understood  as  serving  notice  upon  the  person  who 
undertakes  to  interpret  the  proposition  that  S  and 
P  are  not  separate  and  distinct  things,  but,  for  the 
purposes  for  which  the  proposition  is  expressed, 
one  and  inseparable.  The  proposition,  that  is,  does 


THE   PROPOSITION  95 

not  tell  us  about  any  S,  but  only  about  the  S  that 
is  P. 

The  Existential  View.  This  view  arises  out  of 
the  fact  that  'is,'  besides  serving  as  "a  sign  of  pred- 
ication," has  also  a  meaning  of  its  own,  namely, 
existence.  Thus,  if  we  say  that,  'Aristotle  is  the 
father  of  formal  logic,'  it  may  seem  that  we  are  not 
merely  stating  the  relation  of  Aristotle  to  the  science 
of  logic,  but  are  also  asserting  the  existence  of  Aris- 
totle. For  if  we  do  not  believe  in  the  reality  of  Aris- 
totle, what  significance,  it  may  be  asked,  can  belong 
to  the  statement  that  he  is  the  founder  of  formal 
logic?  To  preserve  the  proposition,  therefore,  from 
evaporating  into  mere  nonsense,  we  seem  forced  to 
admit  that  the  reality  of  the  subject  term  must  be 
secured  by  the  structural  character  of  the  proposi- 
tion itself.  Thus,  if  we  consider  the  structural  for- 
mula, 'S  is  P,'  we  must,  from  this  point  of  view, 
interpret  it  as  meaning,  'S  is,  and  it  is  P.'  That  is 
to  say,  the  significance  of  the  predication,  'S  is  P,' 
depends  upon  our  right  to  take  the  copula  twice 
over,  and  in  each  case  with  a  different  meaning.  In 
the  first  case,  'S  is'  is  equivalent  to  'S  exists ;'  in  the 
second,  'S  is  P/  'is'  is  "a  sign  of  predication,"  in 
the  sense  already  explained.  This,  in  brief,  is  the 
existential  view  of  the  copula. 

It  is  evident  that  we  can  accept  this  view  only 
if  we  take  the  copula  in  the  same  double  way  in  all 
propositions.  But  this  we  can  not  do.  There  are 
some  propositions  whose  terms  forbid  this  interpre- 
tation of  their  copula.  When,  to  take  Mill's  example, 


96  A  TEXT-BOOK  OF  LOGIC 

we  say  that  'A  centaur  is  a  fiction  of  the  poets,' 
existence  is  explicitly  denied,  but  it  is  no  less  ex- 
cluded when,  explaining  a  name,  we  say,  'A  couch 
is  an  article  of  furniture  used  for  reclining/  Fur- 
ther, if  we  say  that  'Shakespeare's  Henry  V  is  nobly 
drawn/  we  are  obviously  moving  in  the  sphere  of 
fiction,  as  we  are  moving  in  the  realm  of  mythology 
when  we  say  that  'Zeus  is  king  of  all  the  gods.'  In 
cases  like  the  foregoing,  the  existential  interpreta- 
tion of  the  copula  seems  to  be  without  meaning; 
but  this  is  so  not  because  'is'  has  lost  the  meaning 
of  existence,  but  because  the  terms  of  the  proposi- 
tion will  not  support  such  an  interpretation.  Thus 
we  see  that  the  effort  to  give  the  copula  a  distinctive 
sense,  over  and  above  what  it  has  as  "a  sign  of 
predication,"  breaks  down  before  the  controlling 
influence  of  the  terms  which  constitute  our  proposi- 
tions. As  we  have  seen,  propositions  are  statements 
of  the  relationship  of  terms,  and  the  relations  are 
determined  not  by  any  special  meaning  carried  by 
the  copula,  but  by  the  character  of  the  terms  that 
enter  into  propositional  statements. 

To  meet  these  difficulties,  it  is  sometimes  pointed 
out  that,  for  speaker  and  hearer  alike,  all  motive 
for  judgment  is  taken  away  unless  we  presuppose 
the  reality  of  the  subject-matter  of  our  judgments. 
We  do  not  express  judgments,  it  is  said,  about  sub- 
jects which  we  believe  do  not  exist.  This  may  be 
readily  granted ;  but  we  should  remark,  at  the  same 
time,  that  it  is  one  thing  to  admit  that  existence 
is  presupposed  by  our  judgments,  and  quite  another 


THE   PROPOSITION  97 

to  affirm  that  reality  is  asserted  by  the  copula  of 
the  propositions  in  which  our  judgments  are  ex- 
pressed. Judgments  may  imply  reality  without  as- 
serting reality.  Belief  in  the  reality  of  Columbus, 
for  example,  is  implied  in  the  statement  that  'Co- 
lumbus is  the  discoverer  of  America ;'  but  what  the 
statement  asserts  is  that  he  discovered  America. 
And  what  is  true  of  this  case,  is  substantially  true 
of  every  case  of  the  judgment. 

If,  then,  we  must  hold  that  belief  in  reality  is 
presupposed  by  every  judgment,  it  is  obvious  that 
we  cannot  mean  the  same  thing  by  existence  in 
every  case  of  judgment.  In  the  examples,  'Utopia 
is  the  ideal  commonwealth  as  depicted  by  More/  and 
The  sun  is  the  centre  of  our  solar  system,'  we  can 
not  be  supposed  to  imply  that  'The  sun'  and  'Utopia' 
belong  to  the  same  sphere  of  existence  or  reality. 
In  other  words,  we  must  recognise  different  spheres 
of  reality,  and  it  is  existence  within  one  or  other 
of  these  spheres  that  is  implied  in  every  judgment 
that  we  make.  Thus,  'Utopia'  belongs  to  the  world 
of  the  imagination ;  'The  sun'  to  the  world  of  phys- 
ical objects.  This  is  a  doctrine  of  logical  importance, 
for  we  may  remark  that  ambiguity,  misunder- 
standing, and  error  arise  when  what  a  judgment 
asserts  as  true  within  one  sphere  of  reality  is  taken 
as  true  within  another  with  respect  to  which  the 
judgment  has  not  been  determined.  If,  for  example, 
I  say  that  'I  believe  in  the  reality  of  Santa  Claus,' 
I  am,  of  course,  asserting  a  belief  which  falls  within 


98  A   TEXT-BOOK   OF  LOGIC 

the  world  of  ideas;  but  if  you  understand  me  to 
imply  the  corporeal  and  individual  existence  of 
Santa  Glaus,  you  only  emphasise  your  misunder- 
standing1 of  what  I  asserted  if  you  challenge  me  to 
produce  him,  or  to  have  him  as  my  guest  on  Christ- 
mas Day.. 

We  may,  then,  sum  up  this  discussion  in  the  fol- 
lowing statements :  (1)  the  copula  does  not  express 
existence,  but  is  only  'a  sign  of  predication;'  (2) 
reality  of  their  subject-matter  is  presupposed  —  not 
expressed  —  by  all  our  judgments;  (3)  there  are 
different  spheres  of  reality  within  which  the  mean- 
ing of  our  several  judgments  is  to  be  determined; 
and  (4)  a  failure  to  refer  any  judgment  to  its  proper 
or  intended  sphere  of  reality  leads  to  ambiguity, 
misunderstanding,  and  error. 

Kinds  of  Propositions.  There  are  three  main 
types  of  propositions;  the  categorical,  the  dis- 
junctive, and  the  hypothetical.  In  this  section  we 
shall  limit  ourselves  to  the  task  of  characterising 
each  kind  of  proposition,  reserving  for  other  chap- 
ters the  discussion  of  the  logical  problems  which 
are  connected  with  these  forms  of  statement.  In 
the  first  place,  however,  it  should  be  remembered 
that  we  are  considering  propositions  in  general,  and 
that,  however  the  categorical,  the  disjunctive,  and 
the  hypothetical  propositions  differ  from  each  other, 
they  all  share  the  common  characteristics  of  propo- 
sitions. It  is,  we  have  seen,  the  business  of  propo- 
sitions to  express  the  affirmative  or  negative  rela- 
tions between  the  objects  of  our  experience  when 


THE   PROPOSITION  99 

these  relations  have  become  explicit  in  judgment. 
This  function  of  the  proposition  is  called  in  logic 
'predication.'  In  every  proposition  P  is  predicated 
of  S,  and  as  we  have  seen,  the  copula  is  the  sign 
of  such  predication.  With  respect,  therefore,  to  the 
three  types  of  proposition  we  may  say  that  they 
differ,  if  they  differ  at  all,  by  reason  of  the  differ- 
ence in  the  forms  of  their  predication.  And  this  is 
the  usual  way  of  distinguishing  them.  Thus,  in  the 
categorical  proposition  we  have  simple  predication ; 
in  the  disjunctive  proposition,  alternative  predica- 
tion; and  in  the  hypothetical  proposition,  condi- 
tional predication.  The  structural  formulae  for 
these  three  kinds  of  proposition  respectively  are: 
'S  is  P ;'  'S  is  either  P  or  Q  or  M ;'  'If  S  is  P,  it  is 
M.'  We  may  also  illustrate  each  kind  by  the  fol- 
lowing examples :  'The  way  of  the  transgressor  is 
hard ;'  'Today  is  either  Monday  or  Tuesday  or  Wed- 
nesday or  etc.;'  'If  Caesar  was  ambitious,  he  de- 
served to  die.' 

Relations  of  the  Main  Types  of  Propositions.  Prop- 
ositions have  been  distinguished  as  either  categor- 
ical, disjunctive,  or  hypothetical.  These  different 
forms  of  proposition  correspond  to  the  different  de- 
grees of  certainty  or  explicitness  of  the  judgments 
they  express.  Now,  since  we  know  more  about 
same  subjects  than  we  do  about  others,  and  our 
knowledge  of  some  parts  of  some  subjects  is  more 
exact  than  it  is  about  other  parts,  we  should  expect 
that  this  fact  would  be  reflected  in  the  propositions 
in  which  we  express  our  several  judgments.  In 


100  A  TEXT-BOOK   OF  LOGIC 

other  words,  the  difference  in  the  forms  of  preposi- 
tional statements  corresponds  to  a  difference  in  the 
explicitness  of  the  knowledge  asserted  by  our  judg- 
ments. There  is  pretty  general  agreement  among 
logicians  as  to  the  foregoing  statement.  There  is 
not,  however,  the  same  harmony  among  them  on  the 
question  of  the  precise  order  in  which  the  several 
types  of  propositions  should  be  arranged.  We 
would  suggest  that  they  may  be  taken,  in  the  order 
of  their  increasing  exactness,  in  the  following  way : 
the  disjunctive,  the  hypothetical,  and  the  categor- 
ical. That  is  to  say,  the  disjunctive  and  the  cate- 
gorical propositions,  respectively,  express  the  least 
and  the  most  explicit  forms  of  knowledge,  and  the 
hypothetical,  to  which  class  most  of  our  judgments 
belong,  will  appear  as  a  form  of  statement  that  ex- 
presses, in  the  majority  of  cases,  the  maximum  at- 
tainable certainty  in  our  quest  for  knowledge. 

To  consider  each  case  separately,  we  may  say  of 
the  disjunctive  proposition  that  it  expresses  uncer- 
tainty as  to  the  details  of  a  subject-matter  which  is 
explicitly  under  consideration.  For  instance,  we 
may  not  be  in  doubt  that  there  will  be  students 
whose  task  it  will  be  to  read  this  paragraph,  but 
we  may  not  be  certain  how  far  they  will  understand 
it.  If,  in  such  a  case,  we  tried  to  make  the  details 
of  judgment  as  precise  as  possible,  our  proposition 
would  then  assume  this  form:  'The  student  who 
reads  this  paragraph  will  either  understand  it,  or 
not  understand  it,  or  misunderstand  it.'  Such  a 
statement,  or  the  judgment  presupposed  by  such  a 


THE   PROPOSITION  101 

statement,  does  not  carry  us  far  on  the  way  to 
knowledge.  It  leaves  us  in  doubt  at  the  point  where, 
if  we  are  to  have  probable  knowledge,  uncertainty 
can  not  exist,  namely,  in  respect  to  the  details  of  the 
judgment's  content.  In  other  words,  the  disjunctive 
proposition  starts  with  a  belief  in  the  reality  of  an 
S,  but  is  uncertain  as  to  what  S  is,  that  is,  whether 
it  is  one  or  other  of  a  number  of  alternatives  which 
are  possible  of  realisation  in  the  sphere  of  existence 
or  reality  covered  by  S.  All  that,  in  such  a  case, 
we  can  say  is  that  'S  is  either  A,  or  B,  or  C,  or  D.' 
If  now  we  consider  the  hypothetical  proposition, 
we  find  that  the  defect  of  the  disjunctive  propo- 
sition has  been  overcome,  and  we  are  no  longer  in 
doubt  as  to  what  we  are  asked  to  believe.  But  we 
also  notice  that  the  greater  explicitness  of  the  rela- 
tions expressed  by  the  proposition  has  been  secured 
by  a  corresponding  loss.  To  consider  the  latter 
point  first,  we  may  observe  that  the  hypothetical 
proposition  does  not  imply,  as  does  the  disjunctive 
proposition,  a  definite  belief  in  the  existence  of  the 
sphere  of  reality  within  which  the  relations  ex- 
pressed by  the  proposition  are  understood  to  fall. 
In  the  case  cited,  for  instance,  the  disjunctive  prop- 
osition started  with  belief  in  the  existence  of  The 
student  who  reads  this  paragraph/  In  the  hypo- 
thetical proposition  the  relations  involved  in  this 
belief  are  used  as  a  condition  of  the  ensuing  judg- 
ment. Thus,  The  student  who  reads  this  paragraph' 
becomes,  in  the  hypothetical  proposition,  'If  a  stu- 
dent reads  this  paragraph/ — a  form  of  statement 


102  A  TEXT-BOOK   OF  LOGIC 

which,  of  course,  leaves  us  uncommitted  as  to 
whether  there  is  any  such  student  or  not.  So  far, 
therefore,  as  the  hypothetical  proposition  is  con- 
cerned, belief  is  never  definitely  implied  in  the  exist- 
ence of  the  sphere  of  reality  within  which  the  rela- 
tions asserted  by  the  judgment  find  their  possible 
realisation.  This,  however,  is  not  an  uncompen- 
sated  limitation.  For,  to  consider  the  other  point 
mentioned  above,  the  meaning  expressed  by  the 
hypothetical  proposition  is  specific;  the  details  with 
which  the  judgment  is  concerned  have  become  de- 
fined in  such  a  way  that  the  conditions  on  which 
belief  rests  form  part  of  what  the  judgment  asserts. 
Thus,  fully  expressed,  the  hypothetical  proposition 
reads,  'If  a  student  reads  this  paragraph,  he  will 
understand  it.'  In  this  case  the  internal  structure, 
the  organic  relations,  of  the  elements  of  thought  are 
more  highly  specialised  than  they  are  in  the  disjunc- 
tive proposition,  and  what  we  are  told  is  that  an 
understanding  of  'this  paragraph'  is  definitely 
grounded  in  the  sphere  of  belief  implied,  although 
indefinitely,  by  the  proposition  itself.  If  we  may 
hold  that  knowledge  grows  by  the  definition  of  de- 
tails, we  shall  have  to  say  that  the  hypothetical 
proposition  expresses  a  higher  type  of  knowledge 
than  the  disjunctive  proposition. 

The  categorical  proposition,  if  it  exists,  carries 
us  outside  the  boundaries  of  probability  into  the 
field  of  certainty.  The  categorical  proposition  com- 
bines certainty  as  to  the  existence  of  the  sphere  of 
reality  which  is  characteristic  of  the  disjunctive 


THE   PROPOSITION  103 

proposition,  and  certainty  as  to  the  detailed  rela- 
tions of  the  matter  of  the  judgment  which  is  charac- 
teristic of  the  hypothetical  judgment.  Hence  our 
proposition  reads,  'The  student  who  reads  this  par- 
agraph, will  understand  it.'  But  in  order  to  under- 
stand the  categorical  proposition,  we  should  observe 
that  our  knowledge  of  any  subject-matter  is  so 
rarely,  if  ever,  complete,  and  that,  in  those  cases 
where  it  is,  the  material  of  judgment  is  likely  to  be 
so  insignificant,  that,  from  the  logical  point  of  view, 
the  categorical  proposition  must  be  held  to  express 
either  an  ideal  limit  of  knowledge,  the  goal  toward 
which  knowledge  is  constantly  advancing  but  never 
quite  reaches;  or  that  it  is  the  least  serviceable, 
because  least  significant,  form  for  the  expression 
of  truth.  We  may,  perhaps,  roughly  indicate  the 
meaning  of  this  remark  by  the  commonplace  obser- 
vation that  an  examination  of  the  forms  of  state- 
ment of  the  poorly  educated  reveals  a  predominance 
of  categorical  propositions;  and,  that,  as  we  rise  in 
the  scale  of  educated  intelligence,  the  other  forms, 
and  especially  the  hypothetical  form,  predominate. 
Dogmatic  statements,  in  other  words,  are  character- 
istic of  the  man  who  does  not  know,  or  of  the  man 
who  knows  things  about  which  no  one  particularly 
cares.  In  either  case,  we  should  have  to  say  that 
such  statements,  from  the  logical  point  of  view,  are 
pseudo-categoricals,  that  they  express  a  belief  which 
either  goes  beyond  or  falls  below  the  range  of  our 
knowledge  of  significant  reality.  But  this  perver- 
sion of  the  categorical  proposition  by  the  ignorant, 


104  A  TEXT-BOOK   OF  LOGIC 

need  not  obscure  for  us  its  proper  logical  position. 
It  does  express  the  form  into  which  knowledge, 
when  it  is  perfect,  would  naturally  fall.  The  cate- 
gorical proposition  implies  belief  in  the  existence 
of  a  sphere  of  reality  within  which  certain  ex- 
pressed relations  are  fulfilled.  It,  however,  remains 
an  ideal  because,  our  knowledge  being  finite,  we 
can  never  get  beyond  the  possibility  of  doubt  as  to 
whether  one  or  other  of  the  conditions  of  the  judg- 
ment has  been  completely  satisfied. 

REFERENCES 

B.  Bosanquet,  The  Essentials  of  Logic,  Lect.  V.,  VI. 

J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Ch.  VI. 
J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Ch.  IX. 
S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  IV. 
W.  Minto,  Logic,  Inductive  and  Deductive,  Part  III.,  Ch.  I. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Ch.  II. 

ADVANCED 

J.  M.  Baldwin,  Thought  and  Things,  Vol.  II.,  Part  II.,  Ch.  VI. 

W.  R.  B.  Gibson,  The  Problem  of  Logic,  Chs.  IX.,  XL,  XII. 

H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Ch.  VII. 

J.  S.  Mill,  A  System  of  Logic,  Book  I.,  Ch.  IV.,  1,  V.,  VI.,  5. 

F.  C.  S.  Schiller,  Formal  Logic,  Ch.  IX. 

C.  Sigwart,  Logic,  Vol.  I.,  Part  I.,  5,  Ch.  II.,  17,  VII. 

J.  Welton,  A  Manual  of  Logic,  Vol.  I.,  Book  I.,  Ch.  I. 

QUESTIONS 

1.  In  what  respect  does  the  proposition  differ  from  the 
judgment? 

2.  What  is  meant  by  the  import  of  a  proposition? 


THE   PROPOSITION  105 

3.  Distinguish  between  the  truth-import  and  the  gtatement- 
import  of  propositions. 

4.  What  light  does  this  distinction  throw  upon  the  inter- 
pretation of  propositions? 

5.  Why  do  we  always  write  the  subject  term  of  a  proposi- 
tion first? 

6.  How  may  we  distinguish  between  the  subject  and  pred- 
icate terms,  and  is  it  always  possible  to  make  this  dis- 
tinction?    Explain. 

7.  What  is  the  logical  difference  between  terms,   names, 
and  words? 

8.  Give  a  logical  classification  of  words. 

9.  What  is  meant  by  single-worded  and  many-worded 
terms? 

10.  What  is  meant  by  saying  that  the  copula  is  the  most 
distinctive  element  of  the  proposition? 

11.  State  and  criticise  the  relational  view  of  the  copula. 

12.  What  are  the  realistic,  nominalistic,  and  conceptualistic 
views  of  the  concept? 

13.  What  is  the  existential  view  of  the  copula,  and  what 
objections  can  be  brought  against  it? 

12.  What  do  you  understand  by  predication?  Characterise 
the  various  kinds  of  predication,  and  show  how  these 
give  rise  to  the  several  types  of  logical  proposition. 

15.  What  are  the  conditions  under  which  we  give  a  disjunc- 
tive expression  to  our  judgments? 

16.  Discuss    the   nature    of   hypothetical   propositions,    and 
show  their  relation  to  disjunctive  propositions. 

17.  Discuss  the  nature  and  limits  of  categorical   proposi- 
tions. 

EXERCISES 

1.  Illustrate,  from  your  own  observation  preferably,  the 
possibility  of  confusing  the  truth-import  with  the  state- 
ment-import of  a  proposition. 

2.  Write  the  following  sentences  in  the  form  of  proposi- 
tions,  indicating   the    subject   and   predicate   terms   in 
each: 


106  A  TEXT-BOOK  OF  LOGIC 

(1)  Over  the  mountains  poured  the  barbarian  horde. 

(2)  The  moonlighh  plays  fitfully  upon  yonder  rippling 
stream. 

(3)  Happy  is  the  man  that  findeth  wisdom. 

(4)  All  is  not  misfortune  that  seems  at  the  moment  un- 
endurable. 

3.  Write  six  sentences  in  which  you  think  it  difficult  or  im- 
possible to  distinguish  the  subject  and  predicate  terms. 

4.  Make  a  list  of  twelve  categorematic  words. 

5.  Write  six  statements  which  show  the  error  of  an  exist- 
ential interpretation  of  the  copula,  and  explain  the  rea- 
son in  each  instance. 

6.  Write  disjunctive  propositions  about  the  following  sub- 
jects: 

(1)  Your  presence  at  a  concert  to  be  given,  say,  next 
week. 

(2)  The  result  of  a  particular  political  election. 

7.  Write  hypothetical  propositions  about  the  following  sub- 
jects: 

(1)  Tomorrow's  weather. 

(2)  The  study  of  the  biological  sciences. 


CHAPTER  IV 

TERMS 

Proposition  and  Terms.  In  the  last  chapter,  we 
defined  a  proposition  as  the  verbal  expression  of  a 
judgment  in  which  something  (P)  is  predicated  of 
something  else  (S).  We  also  analysed  the  propo- 
sition into  its  constituent  factors  —  terms  and  the 
copula  —  and  saw  that  the  relation  which  these  ele- 
ments sustain  to  one  another  is  determined  by  the 
meaning  of  the  proposition  taken  as  a  whole.  The 
proposition,  that  is  to  say,  was  considered  as  deter- 
mining the  existence  and  character  of  its  terms,  and 
not  the  existence  and  character  of  terms  as  deter- 
mining the  existence  and  character  of  the  proposi- 
tion. Terms  are  different  aspects  of  the  meaning 
of  the  proposition  in  which  they  occur.  Expressed 
otherwise,  they  are  functions  of  their  propositions. 
The  further  discussion  of  terms  which  we  begin  in 
this  chapter  must  be  carried  on  in  light  of  these 
general  positions,  and  it  must  be  considered  as  a 
more  detailed  consideration  of  certain  important 
features  of  the  proposition.  The  separate  chapter 
headings  are  employed  merely  for  pedagogic  con- 
venience. 

Connotative  and  Denotative  use  of  Terms.  We  are 
to  consider  at  the  outset  a  distinction  in  the  use  of 
terms  upon  which  hinge  many  of  the  problems  that 
will  come  before  us  in  the  succeeding  pages.  It  is, 

(107) 


108  A   TEXT-BOOK   OF   LOGIC 

therefore,  important  to  give  special  attention  to  the 
precise  logical  significance  that  the  distinction  has, 
and  to  get  clearly  before  ourselves  the  scope  of  its 
application.  The  latter  point  will  be  discussed  in 
the  next  section;  we  shall,  therefore,  confine  our- 
selves here  to  a  statement  and  illustration  of  the 
uses — connotative  and  denotative — to  which  terms, 
whatever  their  character,  may  logically  be  put. 

It  is  part  of  our  common  knowledge  that  words 
are  frequently  used  as  labels  by  means  of  which  we 
identify  things,  and  distinguish  these  things  from 
other  things.  Many  illustrations  will  come  to  mind : 
'the  Rocky  Mountains,'  'the  Amazon  River/  'my  old 
bay  horse,'  etc.  There  is  hardly  any  end  to  the 
number  of  words  which  have  this  use  of  pointing 
to  objects,  and  which  put  us  in  contact  with  par- 
ticular things,  or  groups  of  things.  Now  it  is  this 
fact  of  our  common  speech  that  logic  describes  when 
it  talks  about  the  denotative  use  of  terms.  Terms 
are  used  to  point  out,  refer  to,  or  indicate  objects. 
For  instance,  in  the  statement,  'When  it  comes  to 
packing,  books  are  a  nuisance,'  the  term  'books'  re- 
fers to  the  individuals  of  a  class  of  objects,  and  it 
is,  therefore,  said  to  be  used  denotatively.  In  the 
same  way,  the  term  'lion'  in  the  proposition,  'Lions 
are  carnivorous  animals,'  is  used  to  point  out  this, 
that  or  the  other  particular  lion,  and  the  proposition 
means  that  any  individual  lion  will  be  found  to 
possess  the  specified  characteristics.  Since  the  term 
'lion*  points  out  the  individual  objects  one  has  in 


TERMS  109 

mind  when  the  term  is  used  it  is  said  to  be  used 
denotatively. 

We  may  also  go  to  our  ordinary  employment  of 
language  to  ascertain  what  logic  understands  by  the 
connotative  use  of  terms.  Words,  as  we  know,  not 
only  point  out  objects,  but  they  also  have  meanings. 
When,  for  example,  we  hear  a  strange  word  spoken, 
or  meet  with  it  in  our  reading,  we  ask  what  the 
word  means.  If  no  one  can  tell  us,  we  go  to  the 
dictionary  for  the  information.  Now  we  do  this, 
because  we  have  been  trained  to  expect  that  the 
words  we  meet  will  arouse  some  sort  of  mental 
image,  and  because  experience  has  taught  us  that, 
when  they  do  not,  we  fail  to  understand  what  is 
said  to  us.  That  words  should  have  a  meaning  is 
just  as  important  as  that  they  should  indicate  indi- 
vidual objects.  Unless  such  words  as  Violin,'  'art/ 
'mathematics/  'landscape/  'ocean'  aroused  within  us 
quite  different  images  or  ideas,  we  should  be  at  a 
loss  how  to  use  them,  or  to  understand  them.  Now 
logic  indicates  this  aspect  of  words,  their  meaning 
aspect,  when  it  speaks  of  the  connotative  use  of 
terms.  Terms,  from  this  point  of  view,  are  used  to 
call  up  the  qualities  or  attributes  of  objects.  When 
we  use  a  term  connotatively,  it  must  be  understood, 
consequently,  that  we  are  speaking  about  its  dic- 
tionary meaning.  But,  it  should  also  be  observed, 
the  particular  dictionary  meaning  of  any  term  can 
be  determined  only  from  the  standpoint  of  the  par- 
ticular proposition  in  which  the  term  occurs.  For 
example,  in  Shakespeare's  Coriolanus  we  read,  'She 


110  A   TEXT-BOOK   OF   LOGIC 

will  but  disease  our  better  mirth/  a  passage  in 
which  the  term  'disease'  means  'disturb.'  When 
Locke  writes,  'Although  great  light  be  insufferable 
to  our  eyes,  yet  the  highest  degree  of  darkness  does 
not  disease  them,'  he  is  using  the  same  word  in  the 
sense  of  'cause  suffering  to.'  When,  further,  in 
Thomson's  Summer  we  read, 

Then  wasteful  forth 
Walks  the  dire  power  of  pestilent  disease, 

'disease'  is  used  in  the  more  usual  sense  of  'a  phys- 
ical or  physiological  disorder.'  This  dependence  of 
the  meaning  of  terms  on  their  propositions  is  of 
capital  importance,  and  should  be  kept  constantly 
in  mind. 

Relation  of  the  Connotative  and  Denotative  use 
of  Terms.  The  difficulty  that  is  usually  experienced 
in  understanding  the  doctrine  of  connotation  and 
denotation  is  due  to  the  fact  that  we  do  not  have 
one  group  of  words  whose  use  is  always  connota- 
tive,  and  another  group  of  words  whose  use  is 
always  denotative.  Most,  if  not  all,  terms  are  capa- 
ble of  being  used  in  either  the  one  or  other  of  these 
ways.  But  this  is  not  all.  The  most  important 
fact  to  remark  is  that  in  whichever  of  the  ways 
mentioned  a  given  term  is  employed,  it  is  so  em- 
ployed with  the  other  use  more  or  less  distinctly 
in  mind.  It  would  be  quite  a  fair  statement  of  the 
case  to  say  that  there  is  always  a  reference  of  the 
one  to  the  other,  and  that  in  any  particular  instance 
the  one  implies  the  other.  It  is  not  difficult  to  see, 


TERMS  111 

for  example,  that  the  identification  of  the  individ- 
uals which  are  denoted  by  any  term  depends  upon 
their  possession  of  the  qualities  that  are  connoted 
by  the  same  term.  It  is  also  clear  that  the  qualities 
that  a  term  connotes  are  the  qualities  of  the  individ- 
uals which  the  term  denotes.  Let  us,  for  example, 
examine  the  subject  term  of  the  proposition,  'Man 
is  a  rational  animal.'  If  the  term  'man'  is  used 
denotatively,  that  is,  to  point  out  'Tom,  Dick, 
Harry,  etc.,'  the  proposition  must  mean  that  'Tom, 
Dick,  Harry,  etc.,'  are  the  individuals  in  whom  are 
found  realised  the  qualities  expressed  by  the  pred- 
icate term.  If  the  term  'man'  is  used  connotatively, 
the  proposition  must  mean  that  the  qualities,  'ra- 
tional animal,'  will  be  found  present  in  each  indi- 
vidual, that  is,  in  'Tom,  Dick,  Harry,  etc.'  Let  us 
take,  as  another  case,  'Man  is  a  being  who  volun- 
tarily sets  himself  tasks.'  If,  in  this  proposition, 
the  term  'man'  is  used  to  denote  individual  men, 
then  our  identification  of  the  individuals  who  set 
themselves  tasks  depends  upon  our  knowing  what 
the  qualities  are  which  the  term  'man'  connotes ;  and 
if  it  is  used  to  connote  certain  qualities,  our  under- 
standing of  the  proposition  depends  upon  the  sup- 
position that  these  qualities  can  be  found  in  a  num- 
ber of  discoverable  individuals.  These  illustrations 
serve  to  emphasise  the  general  rule  that  the  con- 
notative  use  of  a  term  does  not  break  away  entirely 
from  its  denotative  use,  or  vice  versa;  and  the  sole 
logical  distinction  between  them  is  that,  in  the  one;, 
we  lay  the  primary  emphasis  on  the 


112  A  TEXT-BOOK   OF  LOGIC 

which  possess  the  qualities,  and,  in  the  other,  on  the 
qualities  possessed  by  the  individuals. 

Another  inquiry  which  conies  before  us  here  is 
whether  this  relation  between  the  connotative  and 
the  denotative  use  of  terms  is  realised  in  all  terms 
whatsoever.  We  can  give  an  answer  to  this  ques- 
tion only  by  anticipating  certain  features  of  the  dis- 
cussion of  terms  contained  in  the  following  pages. 
We  may,  however,  at  this  point  call  attention  to  the 
generally  accepted  position  that  no  term  is  ever  so 
exclusively  denotative  as  to  lose  all  connotation 
whatsoever,  and  that  no  term  can  be  said  to  have 
developed  on  the  side  of  meaning,  i.  e.,  connotatively, 
so  one-sidedly  as  to  have  lost  all  reference  to  objects. 
The  discussion  of  this  question  has  been  brought  to 
the  study  of  proper  names  as  to  a  test  case;  and  it 
is  thought  that  if  the  position  can  be  maintained 
with  respect  to  these  terms,  it  will  be  possible  to 
maintain  it  with  respect  to  other  kinds  of  terms. 
The  question  is  not  a  theoretical  one,  and  we  shall 
gain  nothing  by  considering  it  as  such.  It  is  a 
question  of  fact,  and  can  be  determined  only  by  a 
study  of  each  kind  of  terms  as  it  comes  before  us 
in  this  and  the  following  chapter.  We  may  express 
the  opinion,  however,  that  it  is  quite  possible  that, 
in  the  course  of  time,  the  employment  of  particular 
terms  may  shift  from  a  predominantly  connotative 
to  a  predominantly  denotative  use,  and  there  is  no 
reason,  except  one  of  convenience,  why  all  meaning 
should  not  drop  away  from  some  terms,  and  that 
they  should  stand  in  our  vocabulary  merely  as  sym- 


TERMS  113 

bols  of  the  existence  of  things.  Whether  there  are 
any  such  terms  cannot  be  decided  now;  it  is  more 
important  to  see  that  the  possibility  of  this  being 
the  case  does  not  obscure  for  us  the  more  general 
relation  which  was  expounded  in  the  preceding  para- 
graph. 

A  subject  that  is  usually  discussed  in  this  con- 
nection relates  to  the  changes  that  take  place  in  the 
connotation  and  denotation  of  terms  when  either 
of  these  is  increased  or  decreased.  Under  these 
conditions,  the  changes  in  the  connotation  and  deno- 
tation of  terms  are  said  to  vary  inversely.  More 
fully  stated,  when  the  connotation  of  a  term  is  in- 
creased, its  denotation  is  decreased,  and  vice  versa. 
For  example,  the  denotation  of  the  term  'man'  is  'the 
total  population  of  the  earth/  and  its  connotation, 
we  may  say,  is  'rationality  and  the  upright  position.' 
If  we  increase  the  connotation  by  specifying  'white 
man,'  the  connotation  of  which  term  is  'white,  ra- 
tionality and  upright  position,'  we  decrease  the  de- 
notation which  then  refers  to  'the  white  population 
of  the  earth.'  If  a  further  increase  in  connotation 
is  made  by  specifying  'European  white  man,'  the 
denotation  is  decreased  still  more,  and  indicates  'the 
white  population  of  Europe.'  The  process  thus 
begun  can  be  carried  as  far  as  interest  or  ingenuity 
allows.  The  general  truth  to  which  such  illustra- 
tions point  is  that  the  denotation  of  a  term  is  dimin- 
ished as  its  connotation  is  made  more  definite  by  the 
addition  of  new  attributes ;  and,  conversely,  that 


114  A   TEXT-BOOK   OF  LOGIC 

when  the  connotation  is  decreased  by  dropping  at- 
tributes the  number  of  individuals  to  which  the 
term  applies  is  increased.  This  statement  holds 
good  as  a  general  rule,  but  there  is  no  numerical 
ratio  between  the  increase  or  decrease  of  connota- 
tion and  the  accompanying  decrease  or  increase  of 
the  denotation.  Indeed,  the  denotation  of  a  term 
may  be  increased  greatly  without  any  change  in  its 
connotation,  as  actually  happened,  for  example, 
when  the  British  government  annexed  some  mil- 
lions of  Africans  at  the  close  of  the  Boer  war  with- 
out making  thereby  any  change  at  all  in  the  conno- 
tation of  the  term,  'British  subject.' 

Distribution  of  Terms.  If  we  carry  our  study  of 
the  denotative  use  of  terms  a  step  further,  we  shall 
find  that  the  purposes  which  prompt  our  statements 
sometimes  require  us  to  refer  to  a  determinate  num- 
ber of  the  individuals  denoted  by  the  term,  and  that 
sometimes  our  purpose  is  satisfied  if  we  indicate 
an  indeterminate  number  of  the  individuals  included 
under  the  term.  Let  us  suppose,  for  example,  that 
we  are  discussing  the  theory  of  kingship,  and  that 
I  express  the  belief,  after  Hobbes,  that  the  king  can 
do  no  wrong.  If  this  belief  were  thrown  into  a 
propositional  form,  it  would  become  clear  that  I  am 
thinking  of  all  the  individuals  who  have  exercised, 
or  at  some  time  may  exercise,  the  functions  of  king- 
ship. What  I  mean  is  that  'No  king  can  do  any 
wrong/  that  is,  wrong  doing  cannot  be  predicated 
of  any  king,  —  of  this,  that,  or  of  any  other  indi- 
vidual who  is  or  may  be  a  king.  If  such  a  state- 


TERMS  115 

ment  does  not  recommend  itself  to  your  judgment, 
and  you  express  dissent  from  it,  you  are  not  re- 
quired, by  the  conditions  of  the  situation  which 
determine  your  judgment,  to  concern  yourself  with 
each  and  every  king;  it  will  be  sufficient,  if  wrong 
doing  by  kings  has  ever  occurred,  for  you  to  limit 
your  statement  to  any  of  the  cases  which  contradict 
the  theory  you  oppose.  Expressed  in  a  proposition, 
your  judgment  will  be  'Some  kings  can  do  wrong,' 
or  more  definitely,  'Some  kings  have  done  wrong.' 
You  are  obviously  speaking  of  a  number  of  indi- 
viduals, not  definitely  specified,  who  belong  to  the 
group  denoted  by  the  term  'king.'  The  distinction, 
thus  indicated,  in  the  denotation,  width,  or  extent  of 
terms,  is  known  in  logic  as  the  'distribution'  of 
terms.  By  the  distribution  of  terms  we  mean  the 
consideration  of  terms  from  the  standpoint  of  their 
quantity.  Now,  in  respect  of  quantity,  we  are  lim- 
ited in  logic  by  the  contrast  between  a  definite  and 
an  indefinite  number,  and  the  terms  which  denote 
these  quantities  are  said  to  be  distributed  and  un- 
distributed respectively.  A  term  is  'distributed' 
when,  from  the  form  of  the  proposition  in  which  it 
occurs,  it  is  known  to  refer  to  a  determined  number 
of  individuals  of  the  class  denoted  by  the  term;  it 
is  said  to  be  'undistributed'  when,  from  the  form 
of  the  proposition  in  which  it  occurs,  it  is  known 
to  refer  to  an  undetermined  number  of  the  individ- 
uals of  the  class  denoted  by  the  term.  The  tech- 
nical sign  of  a  distributed  term,  in  an  affirmative 
proposition,  is  'All,'  and,  in  a  negative  proposition, 


116  A   TEXT-BOOK   OF  LOGIC 

'No.'  The  technical  sign  of  an  undistributed  term, 
in  both  affirmative  and  negative  propositions,  is 
'Some.' 

We  have  just  said  that  the  difference  between 
distributed  and  undistributed  terms  is  that  in 
undistributed  terms  the  exact  number  of  in- 
dividuals referred  to  is  left  indefinite,  as,  for 
example,  'Some  birds  are  blue;'  while  in  distributed 
terms  the  number  is  made  definite,  as  for  example, 
'No  man  is  free  from  the  defects  of  his  qualities,' 
and  'Half  my  goods  I  give  to  feed  the  poor.'  We 
shall  have  occasion  to  discuss  this  distinction  again 
when  we  study  the  interpretation  of  propositions; 
but  for  the  present,  it  is  enough  to  remark  that 
neither  in  the  case  of  a  distributed,  nor  in  that  of 
an  undistributed,  term  can  we  say,  from  the  form 
of  the  proposition,  what  the  arithmetical  number 
of  the  individuals  denoted  by  the  term  is.  It  may, 
perhaps,  help  to  make  the  matter  clear  if  we  recall 
that  in  the  study  of  algebra  we  are  taught  to  use 
the  first  letters  of  the  alphabet,  a,  b,  c,  to  represent 
the  known  quantities  of  a  problem,  and  the  last  let- 
ters of  the  alphabet,  x,  y,  z,  to  represent  the  un- 
known quantities.  The  mathematical  difference  be- 
tween these  two  classes  of  quantity,  the  known  and 
the  unknown,  is  the  difference  between  the  dis- 
tributed and  the  undistributed  use  of  terms  in  logic. 
In  the  former  case,  the  known  objects  are  deter- 
minate; in  the  latter,  the  unknown  objects  are  inde- 
terminate. 


TERMS  117 

Some  other  Characteristics  of  Terms.  In  the  fore- 
going paragraphs,  we  have  considered  mainly  those 
features  of  terms  which  are  important  from  the 
point  of  view  of  their  denotation.  There  are  cer- 
tain questions  which  arise  from  the  standpoint  of 
the  connotation  of  terms  to  which  we  shall  direct 
attention  in  the  remainder  of  this  and  in  the  fol- 
lowing chapter.  The  questions  to  which  we  refer 
must  not  be  confused  with  those  that  will  engage 
us  in  a  later  chapter,  and  which  relate  particularly 
to  the  problem  of  definition,  that  is,  to  the  problem 
of  how  the  meaning  of  terms  receives  logical  formu- 
lation. What,  rather,  we  have  to  consider  at  pres- 
ent is  the  fact  that  there  are  certain  general  charac- 
teristics of  terms  which  do  not  depend  upon  the  par- 
ticular meaning  that  terms  have,  but  upon  the 
nature  of  the  interest  which  stimulates  our  judging 
activity.  The  interests  under  which  we  are  led  to 
judge  any  subject-matter  may  require  us  to  express 
what  we  wish  to  say  either  concretely,  abstractly, 
absolutely,  relatively,  positively,  or  negatively. 
That  is  to  say,  our  meaning  may  be  either  concrete, 
abstract,  absolute,  relative,  positive,  or  negative. 
These  distinctions  are  not  coordinate,  and  they  are 
not  at  all  of  equal  importance;  but  the  particular 
relations  which  they  sustain  to  one  another  become 
apparent  only  when  it  is  clear  what  each  signifies. 
We  shall,  therefore,  confine  ourselves,  in  the  main, 
to  stating  how  each  of  these  distinctions  is  to  be 
understood,  and  we  shall  begin  with  the  broadest 


118  A  TEXT-BOOK   OF  LOGIC 

among  them,  the  distinction  between  concrete  and 
abstract  meaning. 

Concrete  Meaning.  One  of  the  most  familiar 
facts  of  our  every  day  life  is  that  we  distinguish 
from  one  another  the  various  objects  that  come 
under  our  observation.  When,  for  example,  we  go 
into  the  city,  we  perceive  the  houses,  the  shops,  the 
traffic  on  the  streets,  and  the  people  on  the  side- 
walks as  quite  different  things.  We  also  carry  over 
into  our  academic  studies  the  endeavor  to  make  dis- 
tinctions, and  to  regard  different  things  as  different. 
Thus,  the  student  of  zoology  learns  to  discriminate 
between  the  blood  vessels,  the  supporting  tissue,  and 
the  characteristic  cells  of  the  specimens  he  observes 
under  the  microscope.  Indeed,  so  general  and  im- 
portant is  this  ability  on  our  part  that  there  is  no 
interest  that  is  not  served  by  it,  and  no  limit  to 
which  it  may  not  be  carried.  For  instance,  we  may 
mark  off  in  this  way  not  only  the  objects  of  the 
material  world,  but  the  qualities  and  relations  of 
these  objects,  and  set  them  before  us  as  distinct  ob- 
jects of  our  thought.  Thus,  'green/  'heavy,'  'but/ 
'cause/  may  become  for  us  objects  as  distinct  as  are 
the  chairs  and  tables  of  our  domestic  life.  Now 
whatever  we  set  off  as  a  distinct  object  of  percep- 
tion or  thought  is  in  logic  considered  as  a  concrete 
object,  and  the  term  that  denotes  such  an  object  is 
called  a  concrete  term. 

It  may  be  observed  that  the  significance  for  logic 
of  the  term  concrete  depends  upon  the  significance 
of  the  word  'thing'  in  the  body  of  our  common 


TERMS  119 

knowledge.  By  a  thing  we  ordinarily  mean  some 
part  of  the  physical  world  which  is  perceived  as  dis- 
tinct from  other  parts  with  which  it  coexists.  Thus, 
the  pictures  on  the  walls  of  our  room,  the  articles 
on  display  in  the  shop  widows,  the  mountains  and 
streams  of  the  landscape,  the  cattle  on  a  thousand 
hill,  are  all  called  'things'  whenever  we  think  of  them 
as  distinct  from  other  objects  with  which  they  are 
associated  in  the  same  common  environment.  But 
the  word  'thing'  is  not  confined  to  objects  of  the 
material  world.  We  also  designate  as  things  what- 
ever can  be  thought  of  as  having  a  distinct  exist- 
ence of  any  kind.  Thus,  if  I  am  trying  to  recall 
something  in  particular  that  has  been  told  me,  I  may 
express  my  impatience  at  not  being  able  to  do  so  by 
saying,  'Why  can't  I  remember  the  thing?'  What  I 
refer  to  here  as  a  thing  is  an  idea.  A  similar  usage 
is  found  in  the  commandment  against  idolatry 
among  the  Hebrews  when  it  is  forbidden  them  to 
make  a  graven  image  "in  the  likeness  of  any  thing 
in  the  heavens  above,"  where  the  word  'heavens' 
has  a  quasi-spiritual  meaning.  Instances  might  be 
multiplied  of  the  very  wide  and  varied  use  to  which 
we  put  the  word  thing  in  popular  speech,  but  those 
given  are  enough  to  emphasise  the  connection  be- 
tween it  and  the  logical  meaning  of  the  term  con- 
crete. 

While,  however,  there  is  this  general  connection 
between  the  two  words,  the  meaning  of  the  term 
concrete  is  more  precise  than  is  the  meaning  of  the 
word  thing.  It  is  true,  for  instance,  that  we  do  not 


120  A  TEXT-BOOK   OF  LOGIC 

ordinarily  refer  to  persons  as  things,  but  logic 
would  have  no  hesitation  in  calling  the  terms,  by 
which  they  were  denoted,  concrete  terms.  On  the 
other  hand,  we  should  describe  as  a  thing  any  object 
of  which  we  could  say  only  that  it  was  in  our  con- 
sciousness, but  unless  we  knew  some  of  its  attri- 
butes or  relations,  we  should  not  be  warranted  log- 
ically in  calling  it  a  concrete  object,  or  the  word 
used  to  denote  it  a  concrete  term.  These  cases  are 
suggestive  of  the  truth  that  it  is  not  mere  existence, 
but  significant  existence  that  logic,  in  the  main,  de- 
notes by  the  term  concrete.  Whenever  an  object  is 
thought  of  as  having  a  definite  kind  of  existence, 
that  is,  as  possessing  certain  qualities  or  standing 
in  such  and  such  relations,  it  is  called  a  concrete 
object,  and  the  words  we  use  to  denote  such  objects 
are  concrete  terms  because  they  are  used  to  connote 
these  qualities  and  relations.  There  are,  as  we  shall 
see,  varying  degrees  of  definiteness  in  the  ways  in 
which  significant  existence  is  asserted,  and  there 
are,  consequently,  several  degrees  of  explicitness  in 
the  meaning  of  the  terms  used  for  denoting  such 
existence.  This  matter  we  shall  discuss  in  the  fol- 
lowing sections;  it  will  be  sufficient,  meanwhile,  if 
the  broad  meaning  of  the  term  concrete  has  been 
made  clear. 

Individual  Meanings:  Proper  Names  and  Desig- 
nations. The  first  class  of  concrete  terms  that  we 
shall  consider  is  that  which  denotes  particular  indi- 
vidual objects.  To  be  able  to  point  out  individual 
objects,  we  must  have  in  mind,  as  a  general  rule, 


TERMS  121 

some  attribute,  or  group  of  attributes,  which  is 
thought  of  as  belonging  to  the  one  object  we  desire 
to  single  out,  and  to  make  the  subject  of  further 
consideration.  The  names  of  such  objects,  when 
they  are  used  as  terms  in  a  proposition,  are  definitely 
denotative  and  explicitly  connotative;  they  point  to 
their  objects  by  means  of  the  attribute  or  attributes 
which  the  term  connotes.  Such  terms  are  called 
individual,  or  singular,  terms. 

Individual  concrete  terms  are  of  two  kinds: 
proper  names  and  designations.  A  proper  name,  to 
consider  that  first,  is  the  name  given  to  an  object  - 
person,  place,  or  thing  —  as  a  special  means  of  dis- 
tinguishing this  object  from  all  other  objects.  We 
give  names  to  the  members  of  our  families,  —  Tom, 
Dick,  Mary,  Sue,  etc.,  to  continents,  mountains, 
rivers,  towns  etc.  We  also  give  names  to  the  horses 
in  our  stables  and  the  cattle  in  our  barns.  There 
is  no  limit,  except  its  usefulness,  to  the  process  of 
naming  the  objects  of  our  acquaintance  in  order  to 
distinguish  them  from  others  with  which  we  do  not 
wish  them  confused.  In  all  such  instances  the 
names  are  proper  names,  and  they  serve  to  individ- 
ualise the  particular  objects  to  which  they  belong. 
When  such  names  are  made  the  subject  of  pred- 
ication they  are  singular  or  individual  terms. 

Now,  about  proper  names,  as  thus  defined,  we 
may  ask  whether  their  designation  of  particular 
objects  is  made  possible  because  they  imply  an  attri- 
bute or  attributes,  that  is,  because  proper  names 
are  connotative.  In  answer  to  this  question,  Mill, 


122  A  TEXT-BOOK   OF  LOGIC 

for  example,  replied  that  proper  names  are  non- 
connotative,  they  can  be  used  only,  he  said,  to  sig- 
nify an  subject.  This  is,  in  many  quarters,  consid- 
ered an  extreme  position,  and  it  may  be  due  to  the 
failure  to  see  that  significance  may  belong  to  a  sub- 
ject not  only  because  of  the  qualities  that  it  pos- 
sesses, but  also  because  of  the  relations  in  which  it 
stands.  "The  very  fact,"  as  Creighton  points  out, 
"that  a  proper  name  is  given  to  an  object  implies 
that  is  possesses  a  certain  marked  individuality," 
and  the  intelligent  use  of  the  name  surely  implies  a 
reference  to  the  qualities  or  relations  by  which  that 
individuality  is  defined.  However,  be  that  as  it  may, 
we  may  admit  that  the  connotation  of  proper  names 
is  ordinarily  quite  general  and  often  vague,  without 
thereby  refusing  to  grant  them  any  significance 
whatever.  If  the  application  of  such  terms  is  un- 
ambiguous, it  is  quite  natural  that  their  meaning 
should  drop  into  the  background  of  consciousness; 
but  if  its  application  should  become  uncertain  or  be 
misunderstood,  we  should  then  feel  the  need  of  mak- 
ing the  connotation  of  the  term  more  definite. 

Individual  concrete  meaning  may  be  expressed, 
in  the  second  place,  by  a  designation.  Logic  regards 
as  a  designation  any  phrase  that  describes  an  object 
by  its  qualities  or  relations,  when  such  phrase  is 
used  for  the  purpose  of  definitely  pointing  out  this 
object.  The  assassin  of  Franz  Ferdinand  of  Aus- 
tria/ 'my  winter  overcoat/  'the  centre  of  the  mate- 
rial universe/  'my  partner/  —  all  these  are  designa- 
tions in  the  sense  defined.  It  is  clear  that  a  desig- 


TERMS  123 

nation  depends  upon  the  appropriateness  of  the  de- 
scription it  embodies  for  the  accurate  identification 
of  the  object  to  which  it  points.  That  is  to  say,  a 
designation  must  be  explicitly  connotative  as  well  as 
definitely  denotative. 

The  wide  usefulness  of  this  method  of  express- 
ing our  individual  concrete  meanings  is  very  evi- 
dent. It  is  true  that,  in  ordinary  life  and  in  scien- 
tific pursuits,  we  need  a  number  of  terms  which 
shall  have  the  specialised  function  of  designating 
particular  individual  objects,  that  is,  terms  that  are 
definitely  proper  names.  But  neither  in  science  nor 
in  daily  life  is  it  necessary  to  assign  proper  names 
to  all  the  objects  that  engage  attention,  and  yet 
some  method  of  referring  to  these  objects  is  neces- 
sary if  we  are  to  develop  the  interests  that  prompt 
us  to  take  note  of  them.  It  is  under  such  circum- 
stances, as  a  general  thing,  that  the  designation 
becomes  of  use.  We  should  be  on  our  guard,  how- 
ever, against  supposing  that  the  objects  to  which 
proper  names  are  assigned  are  necessarily  of  more 
importance  than  those  to  which  we  refer  by  means 
of  designations.  While  it  is  true  that  some  of  the 
objects  which  we  denote  by  designations  are  rela- 
tively insignificant,  this  is  not  always  the  case.  In 
science,  for  instance,  we  speak  of  'the  law  of  grav- 
itation,' 'the  law  of  diminishing  returns/  'cen- 
trifugal force,'  etc.;  and  in  daiy  life  we  use  such 
phrases  as  'the  President  of  the  United  States,'  'the 
Secretary  of  State,'  etc.  These  phrases  are,  accord- 
ing to  the  definition,  designations;  they  point  out 


124  A   TEXT-BOOK   OF  LOGIC 

definite  objects  by  means  of  a  brief  description  of 
the  objects'  characteristics.  They  have,  moreover, 
a  higher  importance  than  some  of  the  objects  to 
which  proper  names  are  given. 

General  Meaning.  The  second  class  of  concrete 
terms,  which  we  have  now  to  consider,  is  character- 
ised by  the  fact  that  the  meaning  conveyed  by  such 
terms  is  applicable  to  more  than  one  object.  Now, 
it  is  true  that,  if  we  were  to  list  all  the  attributes 
of  all  the  objects  of  our  acquaintance,  it  would  be 
found  that  no  one  object  possessed  in  every  respect 
precisely  the  same  qualities  as  any  other.  Every 
object,  in  this  sense,  is  a  unique  object;  and,  if  there 
were  no  other  interest  in  things  than  that  which 
leads  to  the  observation  of  their  uniqueness,  we 
should  have  to  use,  when  speaking  of  such  objects, 
either  proper  names  or  designations.  It  frequently 
happens,  however,  that  our  practical  or  theoretical 
interests  require  us  to  distinguish  among  the  attri- 
butes of  individual  objects  those  that  belong  to 
only  one  individual,  and  those  that  are  possessed  in 
common  by  a  number  of  individuals.  On  the  basis 
of  this  distinction,  we  are  able  to  group  together 
the  objects  which  possess  a  common  set  of  attri- 
butes, and,  conversely,  to  make  the  common  attri- 
butes the  basis  of  our  inclusion  of  other  individuals 
within  particular  groups.  For  example,  we  classify 
certain  animals  as  quadrupeds,  and  certain  others 
as  bipeds,  on  the  ground  that,  amid  an  indefinite 
number  of  differences,  certain  animals  are  alike  in 
the  fact  that  they  walk  on  four  feet,  and  that  cer- 


TERMS  125 

tain  others  are  alike  in  the  fact  that  they  walk  on 
two  feet.  Stated  otherwise,  in  constructing  such 
classes  of  objects,  each  of  the  individuals  belonging 
to  any  one  class  is  thought  of  as  possessing  exactly 
the  same  characteristics  as  any  other  individual  of 
that  class. 

Now  the  names  which  embody  a  meaning  that 
can  be  applied  to  any  one  of  an  indefinite  number  of 
individuals  are  known  in  logic  as  'general'  or  'com- 
mon' terms.  Of  such  terms  we  may  say,  in  view  of 
the  foregoing  discussion,  that  they  are  explicitly 
connotative,  but  indefinitely  denotative.  In  other 
words,  the  attributes  that  a  general  term  connotes 
belong  equally  to  each  and  every  individual  of  a 
group;  but  we  cannot  tell  which  one  or  more  of 
these  individuals  is  denoted,  merely  by  knowing  the 
connotation  of  the  term.  The  characteristic  fact 
about  a  general  term  is,  then,  that  while  its  conno- 
tation or  meaning  is  concrete,  its  application  is 
always  general;  the  meaning,  that  is  to  say,  can  be 
applied  to  an  indefinite  number  of  individuals.  It 
should  be  observed,  however,  that  the  meaning  of 
any  such  term  does  not  exist  apart  from  some  or 
all  of  the  individuals  in  which  this  meaning  is  con- 
cretely embodied.  That  is  to  say,  it  is  the  existence 
of  the  individuals  which  form  the  group  that  deter- 
mines the  meaning  that  any  general  term  may  have. 
Apart  from  these  individuals,  indefinitely  denoted 
though  they  are,  the  general  term  would  lose  all  its 
meaning.  One  reason  for  remarking  this  fact  is 
that  the  interest,  which  leads  us  to  observe  the  com- 


126  A   TEXT-BOOK   OF  LOGIC 

mon  characteristics  of  numbers  of  objects,  is  an 
interest  that  still  recognizes  the  differences  that 
exist  among  the  objects  which  it  groups  together. 
When,  therefore,  these  common  characteristics  are 
expressed  in  general  terms,  it  is  not  to  be  supposed 
that  the  differences  that  distinguish  one  object  from 
another  are  thereby  denied.  What  our  general 
terms  imply  is  that  the  presence  of  individual  dif- 
ferences is  not  inconsistent  with  the  possession,  by 
a  number  of  objects,  of  certain  characteristics  in 
common. 

Collective  Meaning:  Individual  and  General.  We 
have  traced  the  development  of  meaning  from  the 
singular  concrete  to  the  general  concrete,  and  we 
have  seen  that,  in  this  development,  we  have  been 
concerned  with  some  feature  or  features  of  the  indi- 
vidual or  individuals  which  our  interests  prompt  us 
to  study.  For  instance,  our  interest  in  the  differ- 
ences that  exist  between  one  object  and  another  is 
embodied  in  the  meaning  that  singular  terms  have ; 
our  interest  in  the  likenesses  which  exist  along  with 
these  individual  differences  is  expressed  in  the  mean- 
ing that  general  terms  have.  That  is  to  say,  the  de- 
velopment of  meaning  which  leads  from  the  individ- 
ual to  the  general  term  has  been  guided  by  the  con- 
sideration that  we  must  not  do  violence  to  the  differ- 
ences that  exist  between  one  individual  and  another 
while  seeking  for  the  common  ground  of  their  like- 
ness. We  have  now  to  consider  whether,  neglecting 
the  differences  between  individuals,  we  may  start 
with  their  common  likeness,  and  carry  the  develop- 


TERMS  127 

ment  a  step  further.  Or,  to  state  the  inquiry  more 
definitely,  we  may  ask  what  alteration  in  our  mean- 
ing is  made  if  and  when,  in  our  study  of  individuals, 
we  ignore  their  differences,  and  take  note  only  of 
their  likenesses.  We  have  seen  that  we  may  take 
account  of  both  likenesses  and  differences,  and  still 
be  able  to  define  a  meaning  which  applies  to  each  of 
a  number  of  otherwise  dissimilar  individuals.  What 
we  have  now  to  see  is  that  if  we  pay  attention  only 
to  likenesses,  or,  what  amounts  to  the  same  thing, 
consider  only  similar  individuals,  we  are  able  to  de- 
fine a  meaning  which  applies  to  no  one  of  the  indi- 
viduals, but  can  be  intelligently  used  of  all  these  in- 
dividuals taken  together  as  a  whole.  To  illustrate, 
let  us  suppose  that  we  bring  together  in  one  place 
a  number  of  animals  —  lions,  tigers,  elephants, 
jaguars,  ibexes,  zebras,  etc.  Such  a  collec- 
tion we  should  call  a  menagerie.  If,  again, 
we  were  to  bring  together  a  number  of  children 
for  the  purpose  of  educating  them  we  should 
call  such  a  collection  a  school.  There  are  many 
such  collective  groups  of  individuals;  and  we 
can  say  that  the  meaning  of  the  word  by  which  each 
is  indicated  applies  to  none  of  the  individuals  which 
constitute  the  group,  but  only  to  the  group  which  is 
constituted  by  the  individuals.  Thus,  'a  menagerie' 
is  the  name  for  a  particular  group  of  animals,  'a 
school'  is  the  name  for  a  particular  group  of  chil- 
dren under  instruction ;  'the  United  States  of  Amer- 
ica' is  the  name  for  a  particular  group  of  political 
organisations,  etc. 


128  A  TEXT-BOOK  OF  LOGIC 

Now  a  name  which  embodies  a  meaning  that 
can  be  applied  to  a  number  of  similar  individals, 
taken  together  and  thought  of  as  a  whole,  is  called 
in  logic  a  collective  term.  It  is  obvious,  from  what 
has  been  said,  that  the  connotation  or  meaning  of 
collective  terms  is  determined  for  us  by  the  points 
of  observed  similarity  between  the  individuals  which 
constitute  the  groups  which  these  terms  denote. 
Thus,  we  call  a  particular  group  of  individuals  a 
nation  when  we  think  of  all  the  individuals  belong- 
ing to  the  group  as  citizens,  —  citizenship  is  the  one 
attribute  that  all  have  in  common.  We  call  another 
particular  group  of  individuals  a  legislature  when 
we  think  of  all  the  individuals  belonging  to  the 
group  as  makers  of  laws,  —  making  laws  is  the  one 
common  task  in  which  all  its  members  are  engaged. 
The  same  thing,  mutatis  mutandis,  will  be  found 
true  of  all  collective  terms  whatever:  the  connota- 
tion of  such  terms  embodies  certain  observed  sim- 
ilarities between  the  individuals  which  belong  to  the 
groups  which  the  terms  denote. 

When,  on  the  other  hand,  we  consider  the  deno- 
tation of  collective  terms,  it  is  evident  that  the 
groups  which  such  terms  point  out  constitute  a  new 
kind  of  individual,  and  must  be  distinguished  from 
the  individuals  which  are  denoted  by  the  general 
term.  The  individuals  which  general  terms,  as  a 
rule,  denote  are  objects  of  our  ordinary  perception 
and  thought;  they  are  the  things  which,  in  the 
course  of  our  daily  life,  we  are  accustomed  to  take 
as  distinct  objects;  such  things,  we  may  say,  as 


TERMS  129 

each  of  us  has  been  trained  to  observe  in  the  course 
of  the  education  that  the  community  provides.  On 
the  other  hand,  the  individuals  which  collective 
terms  denote  are  individuals  of  a  higher  order,  so 
to  speak;  they  result  from  a  definitely  conscious 
effort  on  our  part  to  bring  together  under  a  single 
view  a  number  of  diverse  things,  and  to  regard  these 
things  as  one  object.  The  objects  which  collective 
terms  denote  are  more  complex  than  those  denoted 
by  the  general  term,  and  should  be  carefully  dis- 
tinguished from  the  latter. 

Collective  concrete  terms  may  be  either  individ- 
ual or  general.  The  individual  collective  term  is 
used  to  point  out  a  particular  group  of  objects  which 
we  wish  to  distinguish  from  all  other  objects  what- 
ever. The  Rough  Riders/  'the  Gordon  Highlanders,' 
'the  Allies,'  (in  the  present  war  in  Europe)  are 
examples  of  collective  terms  used  in  this  way.  It 
may  be  observed  that  the  individual  collective  term 
always  contains  the  definite  article,  'the,'  as  part  of 
its  verbal  form.  Thus,  'the  committee,'  'the  library,' 
'the  family'  are  collective  terms  used  to  point  out 
particular  distinctive  groups.  The  denotation  of 
these  terms  is  definite.  The  general  collective  term 
is  used  to  indicate  a  particular  kind  or  class  of 
grouped  objects,  and,  therefore,  may  be  applied  to 
any  particular  group  of  objects  which  has  the  char- 
acteristics of  the  class  which  the  term  denotes.  For 
example,  when  the  military  and  naval  forces  of  two 
or  more  nations  act  together  for  the  purpose  of  de- 
9 


130  A  TEXT-BOOK   OF  LOGIC 

feating  a  common  enemey,  these  nations  are  called 
allies.  'Allies'  is  a  collective  term,  and,  in  this  case, 
is  general,  since  we  apply  the  same  name  to  each  of 
the  many  combinations  of  this  character  which  his- 
tory records.  Other  illustrations  of  collective  terms 
which  have  a  general  application  are,  'family,'  'li- 
brary,' 'committee.' 

It  is  sometimes  said  that  the  individual  collective 
can  be  changed  into  a  general  collective  term  by 
substituting  the  indefinite  article,  'a,'  for  the  definite 
article,  'the ;'  or  by  omitting  the  article  without  sub- 
stitution. Thus,  'the  allies,'  which  is  an  individual 
collective  term,  becomes  a  general  collective  term 
by  omitting  'the;'  'the  committee,'  'the  family,'  'the 
library'  become  general  by  substituting  'a'  for  'the' 
in  each  instance,  —  'a  committee,'  'a  family,'  'a  li- 
brary.' Sometimes,  however,  the  connotation  of  a 
collective  term  has  become  so  highly  specialised  that 
it  is  capable  of  being  applied  to  only  a  single  object, 
and  in  that  case  it  cannot  be  used,  by  any  change 
whatever,  as  a  general  term.  Examples  of  this  are : 
'the  Congressional  Library  at  Washington,'  'the 
family  of  King  George  IV,'  'the  Committee  on  For- 
eign Relations  in  the  Sixty-third  Congress.' 

Abstract  Meaning.  In  the  foregoing  sections,  we 
have  studied  how  concrete  meaning  develops,  and 
have  seen  that  such  meaning  may  assume  one  of 
three  forms,  or,  as  we  may  say,  indicate  one  of 
three  kinds  of  objects :  —  individual,  general,  or 
collective.  We  have  said  that,  in  these  instances, 
the  meaning  is  concrete  because,  in  each  of  them, 


TERMS  131 

the  connection  between  attribute  and  object  is 
particularly  direct  and  intimate,  although  the  con- 
nection is  in  differing  degrees  of  intimacy.  Any 
meaning  is  considered  concrete  which  conveys  the 
idea  that  'these  are  the  attributes  which  such  or 
such  an  object  has/  or  that  'this  is  the  object  which 
has  such  or  such  attributes/  It  has  been  shown 
that  the  object,  in  some  instances,  is  a  material  ob- 
ject; in  others,  it  is  mental.  But  so  long  as  the 
meaning  we  wish  to  express  is  concrete,  we  always 
suppose  that  we  can  pass  from  object  to  attribute, 
or  from  attribute  to  object,  without  a  break,  or  that 
the  connection  between  attribute  and  object  is  un- 
equivocal. In  other  words,  whenever  we  take  an 
object  in  connection  with  its  attributes,  or  think  of 
attributes  only  in  connection  with  their  objects,  our 
meaning  is  concrete.  If,  however,  we  were  to  con- 
sider attributes  apart  from  objects,  we  should  con- 
front a  new  situation,  and  one  which  would  involve 
a  new  set  of  problems,  the  consideration  of  which, 
in  the  end,  would  lead  us  to  define  a  new  kind  of 
meaning  which,  in  contrast  to  concrete,  might  ap- 
propriately be  called  'abstract.'  For  by  abstract 
meaning  we  commonly  understand  the  idea  of  an 
attribute  —  quality  or  relation  —  thought  of  inde- 
pendently of  the  particular  object  or  objects  of 
which  it  is  the  attribute. 

Now,  when  we  look  at  the  possibility  of  the  ex- 
istence of  such  meanings  as  this,  we  are  confronted 
with  the  danger  of  meaning  less  than  we  actually 
say.  For  instance,  some  logicians  have  defined  the 


132  A  TEXr  •"*'  LOGIC 

terms  in  which  jstract  meanings  are  expressed 

—  'abstract  te  ,,  as  they  are  called  —  as  those 
which  apply  to  objects  thought  of  apart  from  the 
whole  to  which  they  belong,  or  to  attributes  which 
are  thought  of  apart  from  the  objects  of  which  they 
are  the  attributes.  Thus,  a  'leaf  thought  of  apart 
from  the  tree  on  which  it  grows  is,  according  to  this 
definition,  an  abstract  term,  and  'green/  if  it  is  not 
thought  of  as  the  color  of  this  particular  leaf,  or  of 
any  other  particular  green  object,  is  likewise  an 
abstract  term.  In  our  view,  this  is  a  very  mislead- 
ing statement  of  what  abstract  meanings  and  terms 
are.  For  instance,  in  the  cases  just  mentioned,  both 
'leaf*  and  'green'  are  concrete  general  terms.  The 
one  is  the  name  of  an  object,  the  other  of  an  attri- 
bute, and  although  these  terms  are  not  thought  of 
as  belonging  to  any  one  particular  object,  still  they 
are  thought  of  as  belonging  to  any  one  of  an  in- 
definite number  of  particular  objects;  unless  we 
think  of  them  in  this  way  we  cannot  think  of  them 
at  all.  But  if  this  is  what  we  are  to  understand  by 
an  abstract  term,  then  abstract  are  not  distinct 
from  general  terms,  and  have  to  be  classed  as  such. 
Although  the  view  we  have  just  criticised  is  apt 
to  be  misleading  if  it  is  taken  as  providing  a  defin- 
ition of  what  abstract  meaning  is,  it  may  neverthe- 
less serve  a  useful  purpose  if  it  indicates  how  such 
a  meaning  is  developed.  It  is  true  that  in  order  to 
make  our  meanings  abstract,  we  have  to  take  attri- 
butes and  objects  apart  from  their  mutual  impli- 
cation of  each  other;  but  merely  to  take  objects  or 


133 


attributes  in  isolation  is  not,  ,  if,  sufficient  to 

secure  a  new  logical  product.  Tht  Difficulty  of  such 
a  view  as  we  are  criticising  can  be  seen  if  we 
observe  what  would  follow  from  its  acceptance. 
For  if,  according  to  this  view,  only  a  meaning 
were  retained,  the  thing  meant  by  it  being  ig- 
nored, we  may  ask  about  this  meaning  whether 
it  is  a  detached  meaning,  —  a  meaning  that  is  not 
the  meaning  of  any  object.  If  we  answer  this  ques- 
tion in  the  affirmative,  as  we  are  required  to  do,  we 
have  opened  the  door  to  all  the  absurdities  that  be- 
long, in  the  popular  understanding  of  the  word,  to 
'abstract'  thought,  —  to  thought,  that  is,  that  has 
nothing  to  do  with  any  definable  reality.  To  illus- 
trate, if  from  a  student  who  comes  for  the  first  time 
to  the  study  of  philosophy,  we  were  to  elicit  by  care- 
ful questioning  what  his  uninstructed  understand- 
ing of  philosophy  is,  we  should  probably  find  that 
for  him  philosophy  is  a  set  of  ideas  more  or  less 
connected  with  one  another,  but  having  little  or  no 
connection  with  anything  else;  and  if,  by  further 
questioning,  we  were  to  get  him  to  state  why  he  had 
undertaken  its  study,  we  should  probably  find  that 
he  looked  upon  it  either  as  a  good  mental  gymnastic, 
or  as  a  field  in  which,  since  no  one  can  ever  be 
right,  he  at  least  can  never  be  wrong,  whatever 
opinions  he  may  hold.  Such  views  are  held  merely 
because  it  is  supposed,  by  those  who  entertain  them, 
that  philosophy  is  a  set  of  ideas  dissociated  from  all 
objects  whatever,  that  it  is,  in  the  popular  under- 
standing of  the  word,  an  'abstract'  subject.  But 


134  A   TEXT-BOOK   OF  LOGIC 

ideas  which  do  not  make  some  object  more  intelli- 
gible cannot  be  saved  from  the  fate  of  oblivion  by 
giving  them  a  name ;  and  we  may  neglect,  as  falling 
below  the  minimum  of  what  knowledge  requires, 
this  understanding  of  the  term  abstract. 

Having  rejected  the  popular  interpretation  of 
the  expression  'abstract  idea/  we  have  to  ask 
whether,  in  fact,  such  ideas  exist,  and  if  they  do, 
under  what  conditions  their  meaning  is  developed. 
In  answering  these  questions,  we  may  remark  that 
the  situation  with  respect  to  abstract  ideas  is  some- 
what as  follows :  If,  concerning  these  ideas,  we  say 
that  they  are  true  of  the  objects  in  connection  with 
which  they  have  been  formulated  already  in  our 
experience,  then  they  are  not  abstract  ideas  at  all ; 
they  are,  as  we  have  seen,  general  ideas ;  and  if  we 
say  that  they  are  ideas  which  mean  nothing,  we 
are  talking  nonsense.  To  illustrate,  let  us  suppose 
that  in  the  spring  of  the  year,  we  are  looking  out 
upon  the  landscape,  and  that  you  remark,  'How 
green  everything  is!'  Here  'green/  as  you  use  it, 
is  a  general  idea.  If,  however,  in  the  midst  of  a 
conversation  on  monometallism,  or  of  an  unbroken 
silence,  I  were  to  say  'green/  you  would  naturally 
ask,  'Green  what?'  And  if  I  replied,  'Green  nothing, 
just  green/  you  would  have  a  right  to  suspect  my 
sanity.  I  can  only  rehabilitate  myself  in  your  re- 
gard by  pointing  out  that  'green'  is  as  possible  an 
object  of  thought  as  'trees'  or  'grass;'  and  this  is, 
without  doubt,  the  course  that,  under  such  circum- 
stances, one  would  take.  Now,  in  this  illustration 


TERMS  135 

we  have  a  clue  to  what  happens  when  a  concrete 
general  idea  has  broken  away  from  its  moorings  in 
the  world  of  concrete  fact:  the  meaning  conveyed 
by  the  general  idea  becomes  at  once  a  new  object 
of  thought,  which  is  capable  of  further  considera- 
tion and  characterisation.  In  brief,  it  is  only  when 
a  general  idea  has,  in  this  way,  been  dealt  with  as 
a  subject  of  predication  that  we  arrive  at  a  true 
abstract  idea.  For  instance,  if  we  take  our  former 
illustration  we  may  observe  that  although  the  grass, 
the  oak,  maple,  sycamore,  and  elm  trees,  the  wind- 
ing river,  etc.,  are  all  'green,'  they  are  not  the  same 
greens;  they  vary,  as  the  psychologist  tells  us,  in 
tint  and  saturation.  Now  if  we  ask,  with  respect 
to  this  fact,  what  we  mean  by  calling  things  admit- 
tedly different  by  the  same  name,  we  shall  have  to 
say  that  there  is  something,  whether  we  can  state 
definitely  what  it  is  or  not,  which  is  common  to  all 
these  objects,  something  which  we  express  by  the 
word  'greenness/  'Greenness'  is  the  abstract  qual- 
ity by  virtue  of  which  any  object  is  called  green,  it 
is  that  which  belongs  as  an  attribute  to  all  greens 
whatsoever.  If,  to  take  another  illustration,  we 
sort  out  the  skeins  of  yarn  for  testing  colour  blind- 
ness, and  ask  what  it  is  that  leads  us  to  consider 
objects  which  give  so  many  different  sensory  im- 
pressions as  belonging  to  a  single  group,  we  should 
doubtless,  answer  colour.  'Colour'  (=colouredness) 
is  the  abstract  quality  by  virtue  of  which  objects 
are  classified  with  regard  to  the  common  visual  im- 
pressions that  they  make.  Again,  'triangle'  is  an 


136  A  TEXT-BOOK   OF  LOGIC 

abstract  idea,  because  it  implies  the  quality  (tri- 
angularity) by  virtue  of  which  three-sided  plane 
figures  are  grouped  together.  These  illustrations 
indicate  with  sufficient  clearness  the  answer  that 
must  be  given  to  the  question  we  are  considering. 
Any  idea  which  denotes  certain  attributes  common 
to  a  group  of  concrete  objects  is  abstract  if,  at  the 
same  time,  it  connotes  the  underlying  ground  of  the 
similarity  which  exists  between  these  attributes. 

REFERENCES 

SEE  THE  END  OF  THE  NEXT  CHAPTER 

QUESTIONS 

1.  What  is  the  relation  of  terms  to  propositions? 

2.  What  is  meant  by  the  connotative  and  denotative  use  of 
terms?     Illustrate. 

3.  Are  terms  ever  used  exclusively  in  a  connotative  or  ex- 
clusively in  a  denotative  sense?     Explain  your  answer. 

4.  In  case  a  term  is  both  connotative  and  denotative,  are 
the  connotation  and  denotation  always  equally  promi- 
nent?    Explain. 

5.  How  does  any  increase  in  the  connotation  of  a  term 
affect  its  denotation,  and  vice  versa? 

6.  What  is  the  relation  of  the  distribution  of  terms  to  the 
connotative  and  denotative  use  of  terms? 

7.  Explain  what  is  meant  by  the  distribution   of  terms, 
being   careful   to   distinguish   between   distributed    and 
undistributed  terms. 

8.  What  is  the  relation  of  the  meaning  of  terms  to  the 
connotative  and  denotative  use  of  terms? 

9.  What  general  characteristics  of  terms  may  be  mentioned 
from  the  standpoint  of  connotation? 


TERMS  137 

10.  Upon  what  do  these  characterictics  particularly  depend? 

11.  How  is  the  problem  of  definition  distinguished? 

12.  Upon  what  fact  of  our  common  experience  does  concrete 
meaning  depend? 

13.  In  what  respects  does  the  term  concrete  differ  from  the 
word  thing? 

14.  What  do  you  understand  by  an  individual  or  singular 
term? 

15.  Name  the  kinds  of  individual  terms. 

16.  Define  and  illustrate  proper  names. 

17.  Are  proper   names   used   connotatively?      Explain   and 
illustrate  your  answer. 

18.  Define  and  illustrate  designations. 

19.  Are  designations  used  connotatively  and  denotatively? 
Explain. 

20.  What  is  the  importance  of  designations? 

21.  Explain  how  meaning  becomes  general,  and  show  that 
in  doing  so  it  remains  concrete. 

22.  What  is  a  general,  or  common,  term?     Illustrate. 

23.  Discuss  the  connotative  and  denotative  use  of  general 
terms. 

24.  Explain  how  meaning  becomes  collective,  and  yet  re- 
mains concrete. 

25.  What  is  a  collective  term?     Illustrate. 

26.  Discuss  the  connotative  and  denotative  use  of  collective 
terms. 

27.  What  is  an  individual  collective  term?     Illustrate. 

28.  What  is  a  general  collective  term?     Illustrate. 

29.  What  is  the  relation   between   individual   and   general 
collective  terms? 

30.  Does  this  relation  always  hold?     Explain. 

31.  How  does  abstract,  differ  from  concrete,  meaning? 

32.  Distinguish  carefully  between  abstract  and  general 
terms. 

33.  Discuss  the  connotative  and  denotative  use  of  abstract 
terms. 


138  A  TEXT-BOOK   OF  LOGIC 


EXERCISES 

1.  What  are  the  connotation  and  denotation  of  the  follow- 
ing terms: 

Gentlemen  my  typewriter     logic 

George  Washington     gratitude  the  University 

2.  Show  by  an  illustration  that  the  denotation  of  a  term 
may  decrease  if  its  connotation  is  increased. 

3.  Classify  in  a  table  all  the  terms  discussed  in  this  chap- 
ter, showing  which  are  coordinate  and  which  are  sub- 
ordinate. 

4.  Write  a  list  of  twelve  concrete  individual  terms,  and 
indicate  which  are  proper  names,  and  which,  if  any, 
are  designations. 

5.  What  kind  of  term  is  'goodness'  in  each  of  the  following 
statements? 

(1)  Goodness  knows  what  we  shall  do. 

(2)  He  did  it  out  of  sheer  goodness. 

6.  Write  a  list  of  six  general  terms. 

7.  Derive,  if  possible,  abstract  terms  from  each  of  those 
that  occur  in  your  answer  to  the  previous  question. 


CHAPTER  V 
TERMS  (CONTINUED) 

The  Purpose  of  the  Chapter.  In  the  previous 
chapter  we  have  traced  the  development  of  meaning 
from  its  concrete  to  its  abstract  form,  and  in  doing 
so  we  have  touched  upon  the  main  principles  that 
control  the  logical  use  of  terms.  There  are,  how- 
ever, a  number  of  other  interests  that  lead  us  to 
consider  objects  and  their  qualities  in  ways  slightly 
different  from  those  already  described,  and  thus  to 
give  our  doctrine  of  meaning,  in  each  case,  a  slightly 
different  emphasis.  In  this  chapter  we  shall  define 
and  illustrate  some  of  these  more  common  interests, 
and  point  out  the  varying  emphasis  that  our  mean- 
ings come  to  have  under  their  guidance. 

The  Basis  of  the  Distinctions  to  be  Studied.  The 
distinctions  in  meaning  that  we  are  to  study  in  this 
chapter,  like  those  studied  in  the  last,  have  a  basis 
in  common  linguistic  usage.  The  basis  of  the  dis- 
tinction of  concrete  and  abstract  meaning  is  the 
fact  that  we  distinguish  between  an  object  and  its 
qualities,  —  between  the  object  that  is  the  possessor 
of  qualities,  and  the  qualities  possessed  by  the  ob- 
ject. The  distinctions  studied  in  the  present  chap- 
ter are  based  on  this  broad  contrast  between  objects 
and  their  qualities,  but  are  not  identical  with  it. 
When,  for  example,  we  have  distinguished  between 
an  object  and  its  qualities,  so  that  we  can  think  of 
the  object  merely  as  having  existence,  and  can  think 
of  qualities  as  possible  characteristics  of  objects 
without  at  the  same  time  identifying  the  objects 

(139) 


140  A   TEXT-BOOK   OF  LOGIC 

of  which  they  are  the  qualities,  we  can  take  a  fur- 
ther step  in  regard  to  objects,  and  consider  whether 
they  do  or  do  not  stand  in  relation  to  other  objects, 
and,  in  regard  to  qualities,  whether  they  do  or  do 
not  belong  to  certain  objects.  In  the  former  case, 
we  ask  whether  the  relation  that  objects  sustain  to 
other  objects  affects  the  meaning  that  such  objects 
have;  and,  in  the  latter,  we  ask  whether  the  pos- 
session or  non-possession  of  certain  qualities  by  ob- 
jects in  any  way  modifies  the  significance  that  such 
objects  have  for  us.  In  the  first  question,  we  are 
concerned  with  what  are  known,  in  logic,  as  abso- 
lute and  relative  terms;  and  in  the  second,  with 
what  are  known  as  positive  and  negative  terms. 

Absolute  and  Relative  Meaning.  This  distinction 
is  one  that  concerns  the  existential  character  of 
objects,  that  is,  objects  considered  with  respect  to 
whether  they  do  or  do  not  depend  for  the  meaning 
they  have  upon  the  relations  in  which  they  stand  to 
other  objects.  Stated  otherwise,  we  are  asking 
whether  it  is  possible  and  useful  to  study  objects 
independently  of  the  connections  they  may  have 
with  other  objects,  and  whether  the  terms  we  use 
to  denote  objects  do  or  do  not  get  part  of  their 
meaning  from  the  relations  which  these  objects  sus- 
tain to  other  objects  that  fall  outside  the  denotation 
of  these  terms  themselves.  The  answer  to  this 
inquiry  is  quite  obvious.  Objects  whose  connection 
with  other  things  is  for  the  time  being  neglected 
may  certainly  be  held  before  the  mind  as  subjects 
of  investigation.  These  objects  may  be  quite  simple, 


TERMS  141 

as  a  chair,  or  they  may  be  quite  complex,  as  the  solar 
system.  But  whenever  a  simple  or  complex  object 
derives  its  importance  for  consciousness  from  the 
fact  that  we  ignore  the  connections  it  may  have  with 
other  existential  things,  it  is  said  to  be  an  inde- 
pendent object.  Now  when  the  names  of  such  objects 
are  used  as  terms  in  a  proposition,  they  are  called 
absolute  terms.  Thus,  all  individual  terms,  whether 
they  denote  single  individuals,  or  single  groups  of 
objects,  are,  in  the  sense  explained,  absolute  terms. 

What  we  should  understand  by  a  relative  term 
is  more  difficult  to  state.  We  shall  first  consider 
the  most  general  aspect  of  this  question.  It  is  quite 
clear,  in  the  first  place,  that  since  the  whole  prob- 
lem of  meaning  rests,  as  we  have  seen,  upon  the 
connection  between  the  connotative  and  denotative 
use  of  terms,  that  there  can  be  no  object  entirely 
devoid  of  qualities,  and  no  quality  which  is  not  the 
quality  of  some  object.  There  is  always  a  relation 
between  these  two  aspects  of  a  term's  meaning. 
Further,  it  is  clear  that  all  our  meanings,  whether 
concrete  or  abstract,  singular  or  general,  are  also 
relative  in  the  sense  that  the  objects  denoted  by 
such  terms  stand  in  relation  to  objects  denoted  by 
other  terms.  Used  in  the  broad  way,  indicated  by 
these  illustrations,  the  word  'relative'  does  not  point 
out  a  particular  logical  distinction,  but  describes  a 
common  characteristic  of  all  human  knowledge 
whatsoever. 

The  term  relative  is  used  in  logic,  in  contrast 
to  absolute,  to  indicate  the  fact  that  part  of  the 
meaning  that  a  term  has  is  derived  from  the  exist- 


142  A  TEXT-BOOK   OF  LOGIC 

ence  of  an  object  that  the  term  itself  does  not  denote. 
Stated  another  way,  a  relative  term  is  one  that 
implies  the  existence  of  some  other  object  than 
the  one  that  the  term  itself  denotes.  It  is  obvious 
that  no  concrete  individual  term  can  be  relative  in 
this  sense.  But  some  concrete  general  terms  are. 
For  example,  the  term  'father'  is  a  concrete  general 
term  since  it  is  a  name  which  applies  to  an  indefinite 
number  of  individuals  in  whom  the  relations  implied 
by  the  name  are  present;  it  is  also  relative  because 
these  relations  are  such  that  they  depend  for  their 
application  not  only  upon  the  existence  of  the  indi- 
vidual to  whom  the  name  is  given,  but  also  upon 
the  existence  of  either  a  son  or  a  daughter.  A  sim- 
ilar double  relationship  exists  in  all  family  connec- 
tions: uncle,  grandfather,  niece,  etc.  We  may  ob- 
serve the  same  thing  in  other  than  the  family  type 
of  social  organisation:  political,  —  king-subject; 
economic,  —  debtor-creditor;  juridical,  --  plaintiff- 
defendant;  commercial,  —  employer-employee;  do- 
mestic, —  master-servant,  etc.  Whether  this  type 
of  relationship  is  ever  found  outside  of  social  organ- 
isations, or  if  found,  whether  they  are  common,  has 
been  questioned.  We  may  point  out  that  some  logi- 
cians have  been  inclined  to  find  the  meaning  of  such 
a  word  as  'mountain'  in  the  reference  that  it  is  said 
to  contain  to  the  plain  from  which  it  rises.  There 
may  be  other  words  whose  meanings  are  of  this 
relative  sort,  such  as,  right-left,  heavy-light,  up- 
down,  etc.  In  deciding  whether  any  term  is  rela- 
tive, it  should  be  borne  in  mind  that  the  only  clue 


TERMS  143 

that  is  of  logical  value,  is  the  sense  in  which  it  is 
actually  used  in  carefully  guarded  and  intelligent 
speech.  And  by  this  test  it  appears  that  the  words 
whose  meanings  are  determined  by  the  existence  of 
other  objects  than  those  which  such  words  denote 
are  chiefly  those  that  indicate  the  relations  that  we, 
as  human  beings,  have  with  one  another  in  some 
type  of  social  organisation. 

One  other  point  remains  to  be  mentioned.  It  is 
sometimes  found  that  when  one  object  derives  part 
of  its  meaning  from  the  existence  of  another,  the 
latter  also  derives  part  of  its  meaning  from  the 
first.  Not  only,  for  example,  does  uncle  or  aunt 
imply  nephew  or  niece,  but  nephew  or  niece  implies 
uncle  or  aunt.  That  is  to  say,  each  term  of  the 
relation  implies,  and  is  implied  by,  the  other.  Re- 
lationships of  this  kind  are  called  reciprocal.  The 
terms  between  which  such  relationship  holds  are 
also  called  correlatives.  Thus,  when  we  regard  the 
creditor-debtor  relation  from  the  standpoint  of 
creditor,  we  say  that  'debtor'  is  a  correlative  term, 
and  when  we  regard  it  from  the  standpoint  of  debtor, 
we  say  that  'creditor'  is  a  correlative  term.  By  a 
correlative  term,  therefore,  is  meant  that  one  of  a 
pair  of  relative  terms  which  is  implied  by  the  other. 

Positive  and  Negative  Meaning.  The  distinction 
between  positive  and  negative  meaning  rests  upon 
the  answer  we  give  to  the  question  whether  a  given 
object  has  or  has  not  a  certain  attribute  or  set  of 
attributes.  In  a  general  way,  it  is  true  that  every 
object  has  or  has  not  the  attributes  which  the  word 


144  A   TEXT-BOOK   OF   LOGIC 

we  use  to  point  it  out  implies;  otherwise,  it  may 
be  asked,  how  can  we  identify  any  subject  of  dis- 
course? It  may,  however,  be  said  that  it  is  some- 
times necessary  to  state  emphatically  that  the  ob- 
jects we  are  speaking  about  have  or  have  not  cer- 
tain attributes,  and  that  when  this  is  the  case,  the 
meaning  of  what  we  express  is  either  positive  or 
negative.  A  positive  meaning,  to  consider  that  first, 
calls  special  attention  to  the  fact  that  an  object  has 
the  attributes  which  are  implied  by  the  term  which 
is  used  to  point  it  out;  and  it  is  necessary  some- 
times to  emphasise  this  fact,  because  the  meaning 
of  what  we  affirm,  without  such  emphasis,  is  liable 
to  be  misunderstood.  Whenever  the  denotation  of 
a  term  is  unambiguous,  or  when  its  popular  mean- 
ing does  not  render  it  equivocal,  we  do  not  need  to 
call  special  attention  to  its  precise  connotation.  For 
example,  the  term  'rent'  is  popularly  understood  as 
a  fixed  sum  of  money  that  is  paid  or  received  for  the 
occupancy  of  a  house  or  of  land.  It  is  primarily  a 
denotative  term,  and  many  judgments  may  be  ex- 
pressed which  are  perfectly  intelligible  about  the 
object,  —  the  fixed  sum  of  money  —  which  this  term 
denotes.  We  may  say,  for  example,  that  'Rent  is  a 
constant  drain  upon  a  poor  man's  wages/  To  pay 
rent  all  one's  life  is  an  indication  of  improvidence,' 
etc.  In  all  such  instances,  the  sense  of  our  asser- 
tions is  carried  easily  by  the  denotative  use  of  the 
term  'rent.'  However,  when  what  we  assert  is 
dependent,  not  upon  the  object's  existence,  but  upon 
its  meaning,  we  are  in  a  different  position.  In  that 


TERMS  145 

case,  the  meaning  of  the  term  by  which  the  object 
is  denoted  must  be  made  precise  if  we  are  to  have 
an  intelligent  understanding  of  what  a  proposition 
affirms.  Thus,  for  the  economist,  the  term  rent  is 
'the  remuneration  that  is  derived  from  the  concrete 
things  that  have  the  value  of  capital,'  and  this  mean- 
ing of  the  word  must  be  kept  in  mind  in  any  discus- 
sion which  involves  the  idea  for  which  the  term 
stands.  In  this  instance  'rent'  is  used  connotatively, 
and,  so  used,  it  limits  whatever  can  be  said  intelli- 
gently on  any  subject  that  implies  the  idea.  It  is  a 
positive  term  because  it  is  used  to  indicate  the  fact 
that  any  object  to  which  it  is  applied  must  have  the 
qualities  which  the  term  connotes. 

The  Conditions  of  Negative  Meaning.  In  discuss- 
ing negative  meanings,  we  shall  inquire,  in  the  first 
place,  into  the  conditions  under  which  such  mean- 
ings arise.  We  call  attention  to  three  situations 
in  which  knowledge  is  forced  to  assume  a  negative 
form.  First,  whenever,  for  any  reason,  we  fail  to 
reach  a  positive  conclusion  on  any  subject  of  inquiry, 
we  may  map  out  the  progress  of  the  inquiry  by  a 
series  of  negations.  For  example,  let  us  suppose 
that  a  physician  is  called  to  see  a  patient  who  has 
a  serious  illness.  As  the  examination  of  the  patient 
proceeds,  a  number  of  prominent  and  secondary 
symptoms  are  noted  and  the  possibility  of  typhoid, 
tuberculosis,  scarlet  fever,  etc.,  suggest  themselves 
in  turn,  only  to  be  rejected  one  after  the  other; 
and  the  physician  concludes  his  visit  with  a  confes- 
sion, to  himself  if  not  to  the  family  of  the  patient, 
10 


146  A   TEXT-BOOK   OF  LOGIC 

that  he  has  reached  no  positive  knowledge  of  the 
disease,  or  complication  of  diseases,  from  which  the 
patient  is  suffering.  The  physician's  knowledge,  in 
such  a  case,  is  made  up  of  a  series  of  negative  judg- 
ments ;  not  typhoid,  not  scarlet  fever,  etc.  Through 
what  has  been  denied,  that  is,  through  what  the 
physician  calls  his  differential  diagnosis,  he  has 
come  nearer  to,  but  has  not  succeded  in  making,  a 
positive  diagnosis.  Negations  thus  mark  out  the 
limits  within  which  the  positive  characteristics  of  an 
object  are  to  be  found.  No  doubt,  in  new  and  com- 
plicated situations,  business  and  professional  men 
are  often  in  the  position  where  the  only  thing  that 
is  clear  to  them  is  what  not  to  do  or  think.  In  such 
cases,  we  have  negative  but  not  positive  meanings ; 
but  the  former  exist,  not  as  something  opposed  to 
the  latter,  but  as  stages  in  our  progress  toward  it. 
Our  subject-matter  refuses,  one  after  the  other,  a 
number  of  suggested  qualifications,  and  often  we 
have  to  stop  our  investigation  of  the  matter  in 
hand  before  we  have  found  the  particular  qualifi- 
cation which  fits. 

Secondly,  negative  meaning  arises  when  we  safe- 
guard a  positive  meaning  from  misunderstanding 
or  falsification.  Let  us  take,  as  an  example,  the 
case  where  a  new  truth  is  presented  for  the  first 
time  for  our  understanding.  We  are  more  often  in 
this  relation  to  truth,  as  students,  than  in  any  other. 
The  teacher,  let  us  say,  is  expounding  the  psycho- 
logical doctrine  of  perception.  We  follow  him  atten- 
tively as  step  by  step  he  enumerates  and  explains 


TERMS  147 

the  various  factors  in  the  problem,  and  their  relation 
to  each  other.  Now  the  important  question  for  us 
as  students  is  whether  we  have  really  understood 
what  the  teacher  has  said.  Class-room  experience 
shows  that  a  student's  reaction  to  the  subjects  of 
his  study  comes  most  often  in  the  form  of  a  ques- 
tion, or  a  statement,  which,  from  the  teacher's  stand- 
point, is  the  suggestion  of  a  predicate  or  series  of 
predicates,  for  the  topic  of  discourse,  —  in  the  ex- 
ample, the  psychological  doctrine  of  perception ;  and 
the  teacher's  problem  is  to  determine  whether  the 
proposed  predicates  are  compatible  with  those  by 
means  of  which  his  own  exposition  has  been  carried 
on.  Now,  since  our  first  apprehensions  of  any  new 
truth  are  liable  to  be  uncertain,  vague,  or  partial, 
our  proposed  predicates  not  infrequently  endanger 
our  grasp  of  the  new  truth,  and  have  to  be  eliminated 
from  the  list  of  those  attributes  which,  when  taken 
together,  constitute  the  positive  meaning  of  the  sub- 
ject under  consideration.  Now,  this  elimination  of 
incompatible  predicates  is  performed  by  the  teacher 
whenever  he  refuses  to  accept  our  statements  or 
questions  as  elucidations  of  the  subject-matter  in 
hand.  And  his  refusal  is  given  in  the  form  of  a 
negation  which  means,  from  his  point  of  view,  that 
he  is  defending  a  positive  meaning  from  misunder- 
standing or  falsification. 

Thirdly,  negative  meaning  arises  whenever,  in 
carrying  forward  a  special  line  of  work,  our  prob- 
lem is  to  see  how  far,  and  in  what  directions,  our 
subject  is  capable  of  development.  The  starting 


148  A   TEXT-BOOK   OF   LOGIC 

point,  in  a  case  like  this,  is  the  body  of  knowledge 
we  have  already  acquired  about  our  subject.  We  do 
not  become  possessed  of  the  truth  that  lies  beyond 
our  grasp  by  a  method  that  implies  disloyalty  to 
the  truth  that  lies  within  it.  The  working  criterion 
of  the  truth  of  any  thing  new  must  be  the  truth 
that  we  already  possess.  And  this  means  that 
nothing  becomes  true  which  contradicts  what  is 
already  true.  Truth  is  a  system,  systematic  and 
coherent,  one  part  of  which  supports  and  supple- 
ments every  other.  However,  this  position  should 
not  be  held  in  such  a  way  that  the  limitations  of 
the  truth  in  hand  are  allowed  to  make  us  inhospit- 
able to  the  constantly  increasing  and  enlarging  body 
of  truth.  Truth,  it  should  be  borne  in  mind,  grows 
from  less  to  more;  and,  in  the  process,  not  only  do 
we  come  into  possession  of  new  truths,  but  the  old 
truths  are  transformed,  and  sometimes  the  entire 
system  of  truth  changes  its  character.  A  familiar 
instance  of  this  is  the  change  from  the  Ptolemaic 
to  the  Copernican  astronomy.  The  particular  use 
of  the  statement  and  illustration  in  this  place  is  to 
call  attention  to  the  fact  that  such  changes  in  the 
character  and  system  of  truth  is  effected  by  nega- 
tion working  within  the  field  of  established  truth. 
For  what  is  the  recognition  of  truth's  limitations 
but  the  admission  that  negation  not  only  erects  a 
barrier  against  outside  error,  but  also  against  that 
hardening  process  in  the  heart  of  truth  itself  which, 
unchecked,  steels  it  against  the  recognition  of  out- 
side truth?  When,  therefore,  we  are  endeavouring 


TERMS 


to  extend  the  boundaries  of  a  particular  subject,  or 
when  we  have  to  consider  the  truth  of  any  subject 
in  its  relations  to  other  fields  of  knowledge  with 
which  it  may  be  correlated,  we  are  often  forced  into 
the  position  of  either  denying  all  outlying  truths, 
or  modifying,  in  the  interest  of  the  systematisation 
of  truth,  the  knowledge  that  we  already  possess. 
Development  of  knowledge  takes  place  only  when 
we  follow  the  latter  course.  But,  we  should  remark, 
the  modification  of  established  truths,  which  is 
necessary  if  what  is  new  is  to  find  a  place  in  the 
developing  field  of  knowledge,  is  made  possible  by 
the  elimination  of  what  is  erroneous  in  it  ;  or,  stated 
otherwise,  the  limitations  of  existent  truth  are 
brought  to  light  by  negation  working  within  the 
area  of  our  established  beliefs. 

The  Logic  of  Negation.  That  there  is  such  a 
thing  as  negative  meaning  is  not  open  to  serious 
question,  and  what  the  conditions  are  under  which 
it  arises  we  have  already  seen.  The  inquiry  that 
confronts  us  now  is,  How  are  negative  meanings  to 
be  interpreted?  We  may  approach  this  question  by 
remarking  that  negative  meanings  are  developed  out 
of  the  interests  that  lead  us,  in  our  inquiry  into  the 
nature  of  things,  to  affirmative  conclusions.  By 
this  statement  we  mean  that  negation  must  be  inter- 
preted as  a  form  of  knowledge,  and  not  merely  as 
an  assertion  of  the  absence  of  knowledge,  and  that, 
as  such,  it  satisfies,  in  the  particular  instances  in 
which  negative  meanings  arise,  the  motives  that 
sustain  all  our  cognitive  endeavours.  Stated  other- 


150  A  TEXT-BOOK   OF  LOGIC 

wise,  we  may  say  that  since  in  all  knowledge  thought 
is,  as  we  have  seen,  in  some  particular  relation  to 
its  object,  we  must  hold  either  that  this  is  true  of 
negative  as  well  as  of  positive  meanings,  or  that 
negative  meanings  fall  outside  of  the  field  of  logical 
inquiry.  The  only  alternative  to  this  position  would 
be  to  deny  the  existence  of  negation  altogether.  But 
this  we  cannot  do.  And  we  cannot  do  it  for  the 
simple  reason  that  if  we  did  succeed  in  getting  rid 
of  negation  in  one  form,  it  would  break  out  in  an- 
other, —  a  fact  that  is  significant  of  the  distinctive 
function  of  negation  in  our  search  after  the  truth 
of  things.  An  illustration  of  the  fact  just  referred 
to  may  be  found  in  the  endeavour  to  get  rid  of  neg- 
ative meanings  by  reducing  all  propositions  to  a 
common  affirmative  type.  Thus,  it  is  contended,  the 
meaning  of  the  statement,  'Some  men  are  not  Cau- 
casians/ is  not,  'Some  men  are-not  Caucasians,' 
—  a  negative  proposition,  but,  'Some  men  are 
not-Caucasians,' — an  affirmative  propostion.  But,  if 
this  is  true,  it  is  obvious  that,  in  the  latter  case,  the 
predicate  term  has  been  burdened  with  the  negative 
that  belonged,  in  the  former  case,  to  the  copula. 
And,  what  is  more  important,  this  way  of  escape 
from  the  difficulties  of  negative  statements  seems  to 
have  rendered  affirmative  ones  equivocal.  For,  it 
will  be  remembered,  in  all  affirmation  we  are  sup- 
posed to  predicate  a  positive  characteristic,  quality, 
attribute  or  relation  of  a  subject;  but  when  we 
affirm  by  means  of  negative  terms,  we  seem  to  be 
saying  that  the  subject  does  not  possess  the  attri- 


TERMS  151 

butes  connoted  by  the  predicate  of  the  proposi- 
tion which  expresses  our  meaning.  So  far  then 
from  escaping  the  problem  of  negation,  this  attempt 
to  reduce  all  statements  to  an  affirmative  type  forces 
upon  us  the  question  of  how  we  are  to  interpret 
negative  terms.  To  this  question  we  shall  now  give 
attention. 

Let  us  be  perfectly  clear  what  our  problem  is. 
When  we  say  'not-Caucasian/  'not-typhoid,'  etc.,  it 
is  quite  possible,  as  we  have  said,  that  we  mean 
nothing  more  than  that  our  knowledge  is  falling 
short  of  what  knowledge,  strictly  regarded,  requires. 
This,  however,  is  a  different  thing  from  saying  that 
we  have  attained  the  full  measure  of  knowledge 
when  all  that  we  can  affirm  is  that  a  subject  has 
some  quality  or  relation  vaguely  expressed  by  neg- 
ative terms.  When,  for  example,  we  say  of  an  in- 
dividual that  he  is  not-Caucasian,  or  of  a  disease 
that  it  is  not-typhoid,  what,  we  should  like  to  know, 
are  the  positive  attributes,  which  these  terms  con- 
note? And  we  can  ask  such  a  question  just  because 
we  are  dealing  with  an  affirmative  statement. 
Now  one  way  of  answering  this  question  has  been 
to  say  that,  by  the  exclusion  of  a  particular  group 
of  attributes,  expressed  by  the  negative  term,  we 
include  within  the  meaning  that  the  negative  term 
must  have  all  other  attributes  whatsoever.  In  other 
words,  the  negative  term,  or,  as  it  is  sometimes 
called,  the  indefinite,  indesignate,  or  infinite  term, 
is  one  which  divides  all  existing  things  into  two 
groups,  in  one  of  which  there  is  placed  definitely 


152  A   TEXT-BOOK   OF   LOGIC 

the  excluded  meaning,  and  in  the  other  all  other  ex- 
istences and  meanings.  According  to  this  view,  it 
is  the  function  of  the  negative  term  to  denote  the 
latter  group ;  it  is  the  name  of  a  miscellaneous  num- 
ber of  things,  such  as  "accidence  and  adjectives  and 
names  of  Jewish  kings."  Thus,  as  Bosanquet  says, 
"not-Christian  literally  interpreted  includes  not  only 
heathen  humanity,  but  the  fixed  stars,  the  sea,  and 
indeed,  in  Aristotle's  words,  'every  thing  whether 
existent  or  non-existent'  except  Christian.  It  refers 
to  no  one  sphere  in  preference  to  another,  and  thus 
says  nothing  definite  enough  to  be  intelligible."  It 
is  an  example  of  what  we  may  call  bare  negation, 
that  is,  of  negation  unlimited  by  any  reference  to  a 
positive  sphere  of  reality;  and,  because  it  includes 
so  much,  succeeds,  in  the  end,  in  denoting  nothing 
in  particular.  Now  it  may  be  doubted  whether,  out- 
side the  field  of  a  purely  formal  logic,  there  are  any 
such  infinite  terms  as  this;  that  is,  whether  bare 
negation,  a  negation  which  is  not  a  stage  or  step  in 
our  acquisition  or  development  of  positive  knowl- 
edge, is  ever  rooted  in  the  purposes  or  motives 
which,  in  our  relation  to  things,  give  birth  to  rele- 
vant assertion.  But  if  these  infinite  terms  do  not 
'express  meanings  that  are  the  outgrowth  of  the 
motives  that  control  our  knowledge  processes,  if, 
that  is,  they  have  no  relation  to  the  purposes  that 
guide  and  determine  the  life  of  judgment,  they  lose 
all  interest  for  logic ;  they  may  have  a  psychological, 
but  can  have  no  logical,  significance. 


TERMS  153 

Another  way  of  meeting  the  question  we  are 
considering  is  to  point  out  that  the  meaning  of  any 
proposition  must  be  sought  within  the  universe  of 
discourse  which  the  proposition  implies,  and  that, 
consequently,  this  places  a  limitation  upon  the 
meaning  that  the  proposition's  terms  can  have.  If 
from  this  point  of  view  we  consider  the  statement, 
'Some  men  are  not-Caucasian/  it  is  obvious  that  we 
are  speaking  of  men  from  the  standpoint  of  their 
racial  characteristics,  and  that  the  group  of  men 
which  now  interests  us,  —  the  'Some  men'  of  the 
proposition  —  do  not  have  the  characteristics  of  the 
Caucasian.  But  if  we  are  making  the  statement  at 
all  intelligently,  we  mean  more  than  this;  we  mean 
that  they  have  the  characteristics  of  either  one  or 
other  of  the  remaining  divisions  of  the  human  fam- 
ily looked  at  from  the  racial  point  of  view.  That  is 
to  say,  the  positive  meaning  of  the  negative  term 
'not-Caucasian'  can  be  expressed  by  'either  Negro 
or  Mongolian  or  American  Indian.'  Thus,  the  whole 
meaning  of  our  statement  is,  'Some  men  are  not- 
Caucasian,  but  are  either  Negro  or  Mongolian  or 
Indian.'  Likewise  the  other  statement,  'This  dis- 
ease is  not-typhoid,'  means  that  a  pathological  con- 
dition is  present,  but  it  is  not  typhoid  and  it  is  either 
scarlet  fever  or  tuberculosis  or  diphtheria  or  one 
or  other  of  an  indefinite  number  of  the  ills  to  which 
the  human  body  is  subject. 

Privative  Meaning.  Closely  connected  with  nega- 
tive terms  are  those  called  privative,  terms  which 
indicate  the  absence  of  an  attribute  naturally  or 


154  A  TEXT-BOOK  OF  LOGIC 

usually  belonging  to  the  object  which  such  terms  de- 
note. 'Blind/  'maimed/  'orphaned/  'deaf/  are  ex- 
amples. Because  they  are  so  closely  connected,  it 
may  help  us  to  understand  both  negative  and  priva- 
tive terms  if  we  indicate  wherein  they  seem  to  differ 
from  each  other.  The  negative  term,  as  we  have 
seen,  indicates  a  number  of  positive  alternatives  by 
means  of  a  negative  characterisation  of  the  object 
which  such  term  is  made  to  qualify.  It  is,  there- 
fore, not  a  term  that  is  negative  in  meaning  at  all ; 
it  is  only  its  form  that  has  this  characteristic.  The 
reverse  seems  to  be  true  of  privative  terms,  their 
meaning  is  negative,  and  what  is  negated  is  defi- 
nitely the  attribute  or  attributes  which  such  terms 
connote.  Thus,  'The  boy  is  an  orphan/  must  be 
understood  to  mean  that  he  has  no  parents,  —  'the 
absence  of  parents'  being  what  the  term  'orphan' 
connotes.  A  further  difference  between  these  terms 
may  be  indicated.  In  the  case  of  negative  terms, 
we  are  able,  through  what  is  denied,  to  affirm  cer- 
tain alternative  qualities,  that  is,  to  go  beyond  what 
is  definitely  stated  by  such  terms.  In  the  case  of 
privative  terms,  this  is  not  true.  Of  the  boy  who  is 
an  orphan,  all  that  we  can  positively  affirm  is  that 
he  has  no  parents;  we  cannot  say  whether  he  has 
either  a  brother,  or  sister,  or  uncle  or  aunt.  If  of 
any  one  we  can  say,  'He  is  deaf/  we  do  not  find  in 
this  statement  any  ground  of  assertion  with  respect 
to  the  presence,  absence,  or  degree  of  acuteness  of 
any  of  his  other  faculties.  In  view  of  these  charac- 
teristics, privation  must  be  interpreted  as  an  ex- 


TERMS  155 

treme  case  of  negation ;  that  is,  of  a  negation  which 
arises  under  conditions  that  make  defect  of  quality 
a  differentia  of  the  meaning  we  intend  to  convey. 

Disparate  and  Contrary  Meaning.  We  may  touch 
upon  two  other  related  distinctions  which  have  neg- 
ative significance.  Whenever  we  can  divide  a  class 
of  objects  into  a  number  of  mutually  exclusive 
classes,  as,  for  example,  the  class  animal  into  lions, 
tigers,  etc.,  these  subordinate  classes  are  said  to  be 
disparate.  If,  further,  we  can  arrange  the  exclusive 
classes  of  a  group  of  objects  with  respect  to  their 
possessing  more  or  less  of  some  quality,  for  ex- 
ample, organisms  in  a  series  from  amoeba  to  man, 
and  if  we  can  say  of  two  of  these  classes  that,  with 
respect  to  the  common  quality,  they  differ  from 
each  other  in  a  greater  degree  than  either  does 
from  any  other,  the  relationship  between  these  two 
most  differing  classes  is  said  in  logic  to  be  that  of 
contrariety.  A  contrary  relation  is  one  form  of 
negative  meaning,  and  indicates  the  greatest  degree 
of  exclusion,  actual  or  possible,  within  a  single 
genus.  In  other  words,  contraries  are  the  extreme 
limits  of  the  universe  of  discourse  within  which  the 
meaning  of  any  proposition  falls. 

REFERENCES 

H.  A.  Aikins,  The  Principles  of  Logic,  Ch.  V. 

B.  Bosanquet,  The  Essentials  of  Logic,  Lect.  V,  4-7. 

J.  E.  Creighton,  An  Elementary  Logic,  3d  Edition,  Part  I., 
Ch.  IV. 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Chs.  III-V. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  II. 


156  A  TEXT-BOOK  OF  LOGIC 

W.  Minto,  Logic,  Inductive  and  Deductive,  Part  I.,  Ch.  I. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Chs.  III., 

IV. 
W.  J.  Taylor,  Elementary  Logic,  Ch.  II-IV. 

ADVANCED 

J.  M.  Baldwin,  Thought  and  Things,  Vol.  II.,  Part  II.,  Ch. 

VII. 

B.  Bosanquet,  Logic,  Vol.  I.,  pp.  46-71. 
F.  H.  Bradley,  The  Principles  of  Logic,  pp.  155-173. 
W.  R.  B.  Gibson,  The  Problem  of  Logic,  Chs.  I.,  VII.,  VIII. 
H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Chs.  II.,  VI. 
J.  N.  Keynes,   Studies  and  Exercises  in  Formal  Logic,  4th 

Edition,  Part  I.,  Chs.  I.,  II. 
H.  Lotze,  Logic,  Vol.  I.,  Ch.  I. 
J.  S.  Mill,  A  System  of  Logic,  Book  I.,  Ch.  II. 
J.  Venn,  Empirical  Logic,  Ch.  VII. 
J.  Welton,  A  Manual  of  Logic,  Book  I.,  Chs.  I.,  II. 

QUESTIONS. 

1.  How  are  the  logical  distinctions  of  absolute  and  rela- 
tive, positive  and  negative  terms,  related  to  those  dis- 
cussed in  the  previous  chapter? 

2.  Upon  the  answer  to  what  question  does  the  distinction 
of  absolute  and  relative  depend? 

3.  State  and  illustrate  the  meaning  that  belongs  to  abso- 
lute terms. 

4.  What  senses  of  the  term  relative  are  excluded  from  our 
discussion  of  relative  terms? 

5.  What  is  meant  in  logic  by  a  relative  term? 

6.  What  class  of  experience  provides  most  of  our  illustra- 
tions of  relative  terms? 

7.  What  are  correlative  terms? 

8.  Upon  the  answer  to  what  question  does  the  distinction 
of  positive  and  negative  depend? 

9.  What  is  a  positive  term? 

10.     Under  what  conditions  do  we  express  our  meaning  pos- 
itively? 


TERMS  157 

11.  State  and  explain  the  conditions  under  which  our  knowl- 
edge has  to  be  expressed  negatively. 

12.  Are  the  motives  that  lead  to  negative  statements  differ- 
ent from  those  that  lead  to  affirmative  ones?     Explain. 

13.  How  have  some  logicians  tried  to  get  rid  of  negative 
meaning? 

14.  Criticise  this  effort. 

15.  State  and  illustrate  two  views  of  the  logical  significance 
of  negative  terms. 

16.  What  do  you  understand  by  privative  meaning? 

17.  How  are  privative  related  to  negative  terms? 

18.  What   do   you    understand   by   disparate    and   contrary 
meaning? 

EXERCISES 

1.  Write  three  propositions  to  illustrate  the  absolute  mean- 
ing of  terms. 

2.  Discuss  each  absolute  term  in  your  answer  to  the  pre- 
vious question  to  show  whether  it  is  concrete  or  abstract. 
Write  new  propositions  to  illustrate  your  results. 

3.  Write  new  propositions  to  illustrate  concrete  and  ab- 
stract terms. 

4.  Write  three  propositions  to  illustrate  the  relative  mean- 
ing of  terms. 

5.  Discuss  each  relative  term  in  your  answer  to  the  pre- 
vious question  to  show  whether  it  is  concrete,  abstract, 
absolute.     Illustrate. 

6.  Write  three  propositions  to  illustrate  the  positive  mean- 
ing of  terms. 

7.  Discuss  each  positive  term  in  your  answer  to  the  pre- 
vious question  to  show  whether  it  is  concrete,  abstract, 
absolute,  relative.    Illustrate. 

8.  Write  three  propositions  to  illustrate  the  negative  mean- 
ing of  terms. 

9.  Discuss  each  negative  term  in  your  answer  to  the  pre- 
vious question  to  show  whether  it  is  concrete,  abstract, 
absolute,  relative,  positive.    Illustrate, 


CHAPTER  VI 

DEFINITION  AND  THE  PREDICABLES 

The  Questions  of  this  Chapter.  In  our  study  of 
terms,  in  the  two  preceding  chapters,  we  saw  first, 
that  a  term  may  be  used  either  to  point  out  par- 
ticular existing  things  or  to  convey  some  meaning. 
When  a  term  is  employed  to  point  out  particular 
existing  things  it  is  said  to  be  used  denotatively; 
when  it  is  employed  to  convey  some  meaning,  it  is 
said  to  be  used  connotatively.  Arising  out  of  this 
distinction  of  the  denotative  and  connotative  use  of 
terms,  certain  problems  were  forced  upon  us  for 
consideration.  For  instance,  our  study  of  the  deno- 
tative use  of  terms  brought  before  us  the  problem 
of  the  distribution  of  terms,  and  our  study  of  the 
connotative  use  of  terms  brought  to  our  attention 
certain  general  characteristics  of  terms  the  study 
of  which,  as  we  may  now  say,  involved  the  problem 
of  the  classification  of  terms.  In  our  statement  of 
this  latter  problem,  we  were  led  to  recognize  another 
problem,  —  the  (problem  of  definition,  —  and  this 
problem  was  said  to  be  concerned  with  the  way  in 
which  the  particular  meaning  of  terms  receives 
logical  formulation.  The  facts  and  relations  em- 
bodied in  this  statement  of  the  logic  of  terms  may 
be  expressed  in  a  tabular  form  as  follows : 

(158) 


DEFINITION   AND   THE   PREDICABLES  159 

Standpoint  Problem 

Denotation  Distribution  of  terms 

Terms 

f  Classification  of  terms 
Connotation 

^Definition  of  terms 

This  table  may  be  read  as  follows:  Terms  studied 
from  the  standpoint  of  their  denotation  give  rise 
to  the  problem  of  the  distribution  of  terms ;  studied 
from  the  standpoint  of  their  connotation,  they  give 
rise  either  to  the  problem  of  the  classification  of 
terms  or  to  the  problem  of  the  definition  of  terms. 

Of  the  two  problems  connected  with  the  conno- 
tative  use  of  terms,  the  problem  of  the  classification 
and  of  the  definition  of  terms,  the  former  may  be 
said  to  be  concerned  with  the  question,  What  are 
the  various  kinds  of  terms  that  form  the  S  and  P 
of  logical  propositions  ?  And  the  latter  is  concerned 
with  the  question,  What,  irrespective  of  the  kinds 
that  terms  may  be,  are  the  meanings  that  terms  may 
have?  We  have  considered  the  first  of  these  ques- 
tions in  the  two  previous  chapters.  The  second 
question  we  shall  study  in  the  first  part  of  the  pres- 
ent chapter.  In  this  part,  we  shall  try  to  show  how 
to  make  the  particular  meanings  of  the  terms  we 
employ  definite,  how  to  formulate  them  in  such  a 
way  that  no  doubt  remains  as  to  the  sense  in  which 
they  are  used.  We  hope,  as  the  result  of  our  study, 
to  learn  how  to  proceed  when  we  are  required  to 
make  the  meaning  of  any  of  our  terms  explicit. 


160  A  TEXT-BOOK  OF  LOGIC 

After  we  have  concluded  this  study,  we  shall  be  in 
a  position  to  ask  and  answer  the  question,  What 
kinds  of  things  can  be  predicated  of  a  subject? 
The  convenience  of  discussing  this  question  here 
is  that  doubt  has  been  cast  upon  the  possibility  of 
predicating  of  any  subject  its  own  definition.  But 
it  is  more  than  a  question  of  convenience;  for,  as 
we  shall  see,  our  whole  view  of  the  nature  of  defini- 
tion is  involved  in  the  position  we  take  with  respect 
to  the  predicables.  There  are,  then,  two  problems 
to  be  discussed  in  this  chapter,  the  problem  of  defi- 
nition and  the  problem  of  the  predicables,  and  of 
these  the  first  to  be  considered  is  the  problem  of 
definition. 

Non-Ambiguity.  We  may  approach  the  study  of 
this  question  by  calling  attention  to  the  fact  that  in 
the  fields  of  science,  more  than  anywhere  else,  our 
ideas  must  be  accurate,  and  the  language  in  which 
these  ideas  are  expressed  must  definitely  convey  the 
meaning  intended.  That  is  to  say,  the  natural  fluid- 
ity of  language  must  not  be  allowed  to  go  in  the 
sciences  to  the  point  of  ambiguity.  Whenever, 
that  is,  we  wish  to  express  our  ideas  in  words,  there 
is  a  limit  to  the  indefiniteness  that  can  be  allowed 
to  the  forms  of  our  speech,  and  if  we  really  convey 
the  sense  of  what  we  mean  our  words  must  be 
definite  in  what  they  connote. 

This  demand  for  precision  in  the  use  of  words 
may  be  easily  misunderstood,  and  it  may  lead  to  an 
effort  after  the  impossible  or  undesirable.  The  aver- 
age man's  impatience  with  over-primness  of  speech 


DEFINITION   AND   THE   PREDICABLES  161 

is  a  healthy  protest  against  pedantry ;  but  the  same 
man's  laxness  in  the  use  of  words  bears  witness 
quite  often  to  the  vagueness  of  his  ideas.  These  are 
the  extremes  against  which  it  is  desirable  to  guard : 
the  extreme,  on  the  one  hand,  of  an  accuracy  of 
speech  out  of  all  proportion  to  the  character  and 
importance  of  the  subject-matter  of  our  thought; 
and  the  extreme,  on  the  other  hand,  of  being  tyran- 
nised over  by  words  and  of  using  them  as  substi- 
tutes for  ideas.  There  is  always  an  appropriate 
exactness  that  we  should  strive  to  realise  in  our  use 
of  language,  and  nothing  more  than  this  can  be 
demanded  of  us  by  the  strictest  logic.  We  must  aim 
to  make  our  speech  non-ambiguous,  but  non-ambi- 
guity is  relative  to  the  purpose  of  the  speaker  and 
to  the  subject  of  his  thought.  Non-ambiguity 
changes  with  the  change  of  purpose  and  subject, 
and  the  degree  of  exactness  that  is  requisite  on 
some  occasions  and  with  respect  to  some  subjects 
might  be  altogether  inadequate  if  these  were  differ- 
ent. There  is  no  one  standard  of  explicitness  that 
we  are  required  to  attain ;  the  most  that  can  be  de- 
manded is  that  on  all  occasions,  and  with  respect 
to  all  subjects,  our  language  be  made  a  fitting  ve- 
hicle for  the  expression  of  the  ideas  we  wish  to 
convey. 

We  have   called   attention   to   these  somewhat 
obviaus  considerations,  because,  through  their  neg- 
lect, the  importance  of  the  problems  with  which  we 
are  here  concerned  has  frequently  been  obscured. 
11 


162  A   TEXT-BOOK   OF  LOGIC 

This,  we  think,  is  unfortunate;  for  whatever  can 
help  us  to  avoid  misunderstanding,  whatever  can 
strengthen  our  reputation  for  saying  what  we  mean 
and  meaning  what  we  say,  cannot  be  of  indifference 
to  any  one  of  us,  in  a  world  where  intellectual  integ- 
rity is  coming  to  play  an  increasingly  important 
part. 

These  considerations  may  also  enable  us  to  see 
that  whenever  we  are  in  danger  of  being  misunder- 
stood, whether  in  science  or  literature  or  business, 
on  account  of  the  indefinite  meanings  of  the  words 
we  employ,  there  is  required  some  method  by  which 
the  misunderstanding  can  be  avoided,  some  method 
by  which  words  can  be  moulded  to  the  uses  of  ideas. 
Life  is  one,  and  the  occasions  when  it  is  necessary 
to  state  explicitly  the  meaning  of  the  words  we  use 
arise  all  along  its  way,  and  are  not  confined  to,  even 
if  they  are  more  frequent  and  more  urgent  in,  the 
various  departments  into  which  our  human  knowl- 
edge has  been  organised.  In  other  words,  ambiguity 
may  be  as  undesirable  in  the  drawing-room  or 
counting-house  as  in  the  laboratory,  and  whenever 
and  wherever  it  is  a  hindrance,  we  naturally  try 
to  get  rid  of  it.  But  before  we  consider  how  this 
may  be  done,  a  word  may  be  added  on  ambiguity 
itself. 

Ambiguity.  The  traditional  doctrine  of  ambi- 
guity may  be  briefly  stated.  Any  term  is  ambig- 
uous if  it  is  given  a  meaning  in  a  proposition  which 
it  does  not  have  in  the  judgment  which  the  prop- 
osition expresses.  For  example,  'He  was  a  man  who 


DEFINITION   AND   THE   PREDICABLES  163 

always  chose  a  mean  line  of  action.'  Terms  that 
have  more  than  one  meaning,  and  which,  therefore, 
lead  to  ambiguity  of  statement,  are  called  ambig- 
uous or  equivocal;  and,  in  contrast  to  these,  those 
that  have  only  one  meaning  are  called  unambig- 
uous or  univocal. 

There  are  two  respects  in  which  this  view  of 
ambiguity  does  not  seem  to  be  satisfactory.  First, 
it  implies  too  formal  or  mechanical  a  view  of  logic. 
It  leaves  the  impression  that  words  are  like  counters 
in  a  game  to  be  pushed  here  and  there  as  the  exi- 
gencies of  the  game  demand,  that  no  difference  is 
made  to  the  words  themselves  by  their  change  of 
relation  in  different  propositions.  Second,  it  sup- 
poses that  there  are  certain  words  which  have  a 
fixed  meaning,  and  that  the  statements  in  which 
they  occur  are,  therefore,  free  from  ambiguity. 
This  is  difficult  to  maintain  for  any  class  of  words, 
and  if  it  were  true  of  particular  words  there  is  no 
guarantee  that  it  must  remain  so.  The  principle 
that  should  guide  us  in  a  discussion  like  this  is  that 
it  is  not  words  that  make  a  language,  but  language 
that  moulds  words  and  fits  them  to  the  uses  for 
which  the  language  exists.  For  example,  the  word 
'Democrat'  has  a  definite  historical  meaning,  as  also 
has  the  word  'Republican' ;  but  as  names  of  political 
parties  they  no  longer  mean  what  they  meant  origin- 
ally, and  have  become  vague  and  indefinite  through 
the  growth  within  each  party  of  sub-classes  or 
varieties  of  democracy  and  republicanism,  each  of 
which  would  deny  to  the  other  the  right  to  the  name. 


164  A  TEXT-BOOK   OF  LOGIC 

This  process  of  splitting  off  from  a  perfectly  clear 
centre  of  meaning  is  going  on  all  the  time  in  the 
living  languages  of  the  world,  and  is  giving  rise  to 
conflicting  meanings  in  the  uses  of  words. 

The  problem  of  ambiguity  may  be  viewed  in  a 
broader  way  still.  Instead  of  considering  it  as  hav- 
ing to  do  with  the  indefiniteness  that  arises  from  the 
vague  or  shifting  meaning  of  words,  we  may  view 
it  as  in  some  sort  the  central  or  fundamental  prob- 
lem of  the  science  of  logic  itself.  For  logic,  as  we 
have  seen,  is  a  study  of  the  methods  by  which  mean- 
ings can  get  asserted,  and  how  asserted  meanings 
can  get  expressed  in  propositions.  It  is  because 
meaning  tends  to  elude  us,  and  because  words  are 
not  always,  if  they  are  ever,  faithful  representatives 
of  ideas,  because,  that  is  to  say,  ideas  and  words 
are  both  equivocal,  that  we  are  compelled,  if  the 
aims  of  thinking  are  to  be  attained,  to  study  the 
sources  of  this  uncertainty,  and  to  derive  guidance 
from  the  knowledge  that  we  thus  obtain.  Ambi- 
guity, therefore,  is  a  term  that  describes  a  natural 
condition  of  human  thinking,  as  well  as  a  natural 
indefiniteness  of  human  speech.  But,  as  we  all 
know,  vagueness  in  an  idea  and  indefiniteness  in 
speech,  have  many  sources ;  and  it  will  not  be  until 
we  have  reached  the  end  of  our  studies  that  we 
shall  have  reviewed  even  the  more  important  ones. 
Ambiguity  in  the  meaning  and  application  of  words, 
therefore,  is  part  of  a  much  larger  problem ;  but  in 
this  chapter  we  shall  consider  only  the  ambiguity 
that  arises  in  connection  with  our  use  of  words. 


DEFINITION  AND  THE   PREDICABLES  165 

Translation.  One  of  the  most  common  means  for 
the  removal  of  ambiguity  is  translation.  Thus,  if 
what  we  say  is  not  understood,  or  is  in  danger  of 
being  misunderstood,  we  often  translate  the  same 
idea  into  another  set  of  words  in  the  hope  that  the 
ambiguity  may  be  removed.  This  is  a  common  prac- 
tice both  in  literature  and  in  ordinary  conversation. 
When,  for  example,  Shakespeare  makes  Hamlet  say, 

O,  that  this  too  too  solid  flesh  would  melt, 
Thaw,  and  resolve  itself  into  a  dew; 
Or  that  the  Everlasting  had  not  fixed 
His  canon  'gainst  self-slaughter! 

he  is  putting  into  Hamlet's  mouth  words  that  ex- 
press a  single  idea  twice  over,  namely,  the  longing 
for  death  as  a  means  of  escape  from  his  troubles. 
If,  again,  a  teacher  should  ask  his  class  a  question 
which  fails  to  elicit  the  correct  answer,  he  would 
probably  restate  the  question  in  the  light  of  the 
difficulties  that  the  answers  had  thrown  upon  the 
class's  understanding  of  the  question  as  first  stated. 
If  further,  to  take  an  illustration  already  used,  we 
were  to  say  of  a  given  individual,  'He  was  a  man 
who  always  chose  a  mean  line  action,'  and  we  were 
misunderstood  to  say  that  he  was  a  man  'devoid  of 
a  generous  disposition',  we  should  probably  substi- 
tute for  the  word  'mean,'  the  word  'moderate'  in  a 
re-statement  of  what  we  had  intended,  in  the  first 
place,  to  say.  There  is  no  doubt  that  this  habit  of 
translating  into  a  variety  of  forms  the  ideas  we  wish 
to  express  is  so  inveterate  that  most  of  us  talk  more 


166  A  TEXT-BOOK   OF  LOGIC 

than  is  necessary  for  understanding,  and  many  of 
the  books  we  ordinarily  read  are  much  longer  than 
they  need  be.  But  the  care  we  exercise  in  making 
our  meaning  clear  is  grounded  in  a  healthy  instinct ; 
it  is  the  respect  we  pay  to  the  demand  for  unambig- 
uous statements. 

When  Translation  may  be  Employed.  If  we  look 
at  the  class  of  cases  illustrated  in  the  preceding 
paragraph,  we  shall  discover  that  the  source  of  their 
ambiguity  does  not  lie  in  the  fact  that  our  words 
have  a  vague  fringe  of  meaning,  but  that  the  centre 
or  core  of  meaning  has  been  misunderstood.  When- 
ever ambiguity  arises  from  our  unfamiliarity  with 
the  meaning  of  the  words  in  which  ideas  are  ex- 
pressed, what  is  needed  is  that  the  same  idea  be 
translated  into  a  set  of  words  with  the  meaning  of 
which  we  are  familiar. 

In  translation,  then,  ambiguity  arises  from  the 
fact  that  the  central  meaning  of  a  word  is  not  pre- 
cisely determined,  either  because  the  word  carries 
no  meaning  at  all,  or  because  it  carries  a  meaning 
that  renders  the  whole  sentence  indefinite.  If,  for 
example,  you  do  not  know  what  the  word  'com- 
mandeer' means,  you  are  not  likely  to  understand 
any  statement  in  which  the  word  occurs,  for 
example,  'My  motor  has  been  commandeered.'  To 
meet  such  a  situation  it  is  obvious  that  some  other 
word  or  explanatory  statement  would  have  to  be  sub- 
stituted for  the  meaningless  'commandeered.'  If, 
to  take  another  case,  a  class  in  logic  were  given  the 
task  of  stating  the  meaning  of  the  assertion  'Non 


DEFINITION   AND   THE   PREDICABLES  167 

omnis  moriar  (I  shall  not  all  die),'  and  it  proved 
difficult  or  impossible,  the  reason  would  be  that  am- 
biguity spreads  over  the  whole  sentence  from  the 
indefiniteness  of  the  word  'all/  an  indefiniteness 
that  is  not  due,  as  in  the  former  illustration,  to  the 
absence  of  meaning,  but  to  the  conflict  of  two  mean- 
ings that  are  not  clearly  distinguished.  In  this  ex- 
ample, the  Latin  word  omnis  has  a  distributed  mean- 
ing, and  if  the  Roman  had  wished  to  express  the 
collective  meaning  of  'all/  he  would  have  written 
cunctis.  We  have  only,  therefore,  to  point  out  the 
distributed  use  of  the  word  'all'  to  enable  the  student 
to  see  that  the  meaning  of  the  statement  is  'some 
part  of  me  is  immortal/ 

When  Definition  is  Required.  The  conditions  un- 
der which  definition  is  required  are  different  from 
those  under  which  translation  is  most  effective. 
Definition  is  called  for  when  the  work-a-day  mean- 
ing of  the  word  that  requires  defining  is  already 
known,  but  is  becoming  obscured  by  the  fact  that, 
through  the  similarity  of  its  meaning  to  other 
words,  its  distinctive  characteristics  are  in  danger 
of  being  overlooked.  For  instance,  the  most  obvious 
common  characteristic  of  the  violin,  viola,  'cello, 
and  bass  viol  is  their  shape,  and  it  is  this  that 
leads  one  to  regard  all  of  them,  on  first  ac- 
quaintance, as,  let  us  say,  violins.  Our  knowledge, 
that  is  to  say,  emphasises  the  common  likeness  that 
exists  between  the  several  instruments  named,  and 
there  is  confusion  of  one  thing  with  another  because 
the  differences  which  give  to  these  objects  a  distinct 
place  in  the  universe  of  musical  instruments  have 


168  A  TEXT-BOOK   OF  LOGIC 

been  overlooked.  The  confusion  does  not  arise  from 
what  is  included,  but  from  what  is  omitted,  and 
what  is  omitted,  in  this  case,  lies,  outside  the  centre, 
at  the  boundaries  of  the  words'  meanings.  To  state 
it  generally,  the  meanings  of  closely  related  words 
encroach  upon  one  another  when  the  boundaries 
that  keep  their  meanings  distinct  are  overlooked  or 
broken  down.  Now  it  often  happens  that  the  sense 
of  what  we  say  depends  to  a  large  extent  upon  a 
word's  ability  to  suggest  just  such  differences  as, 
in  the  illustration  used,  we  persistently  ignored. 
When  this  happens  ambiguity  is  sure  to  result,  an 
ambiguity,  let  it  be  observed,  that  is  due  to  the  con- 
fusion of  closely  related  things.  In  such  a  case,  the 
practically  important  problem  is  to  find  some 
method  by  which  ambiguity  of  the  kind  here  in 
question  can  be  overcome  when  it  exists,  or  be 
avoided  when  it  does  not. 

The  Method  of  Definition.  In  any  case  of  ambi- 
guity that  can  be  overcome  by  definition,  the  indefi- 
niteness  of  the  word's  meaning  which  occasions  the 
ambiguity  is  due  to  our  failure  to  mark  off  the 
boundaries  of  this  meaning  from  those  of  other  re- 
lated meanings.  Indefiniteness  of  this  sort  in  the 
meanings  of  words  may  be  illustrated  if  we  ask  our- 
selves, for  example,  what  we  understand  by  a  bal- 
loon and  an  air-ship.  The  conspicuous  central  mean- 
ing of  the  two  words  is  doubtless  the  fact  that  they 
are  machines  that  travel  in  the  air ;  but  if  they  mean 
no  more  than  this,  we  shall  very  soon  be  calling  each 
by  the  name  of  the  other,  or  we  shall  be  calling  all 


DEFINITION   AND  THE   PREDICABLES  169 

machines  that  travel  in  the  air  by  the  name  of  the 
one  or  the  other.  It  is  in  cases  like  this,  as  we  have 
seen,  that  the  definition  of  words  is  necessary. 
How,  then,  shall  we  go  about  the  task  of  defining? 
Obviously,  by  the  way  of  comparison,  by  the  com- 
parison of  the  things  which  our  words  denote.  Thus, 
if  we  wish  to  make  our  meanings  of  the  words  bal- 
loon and  air-ship  precise,  we  compare  an  air-ship 
with  a  balloon,  and  this  comparison  will  lead  to  the 
discovery  that  they  differ  from  one  another  in  the 
method  of  their  locomotion:  the  air-ship  is  driven 
by  an  engine  and  the  balloon  is  not.  We  shall,  then, 
call  anything  an  air-ship  which  travels  in  the  air 
and  is  driven  by  an  engine,  and  the  word  balloon 
will  be  reserved  for  any  air-traveling  machine  which 
depends  for  its  locomotion  upon  the  air-currents. 
This  method  of  definition  is  for  all  ordinary  purposes 
the  most  practical,  and  it  lends  itself  to  the  require- 
ments of  the  specific  occasions  which  make  defini- 
tion imperative.  We  get,  that  is  to  say,  the  mean- 
ing that  suits  the  purpose  of  the  statement.  Con- 
stant practice  in  the  comparison  of  what  words 
denote  will  not  only  render  our  meanings  more  pre- 
cise, but  free  us  from  that  indefiniteness  which 
comes  from  an  exclusive  familiarity  with  the  dic- 
tionary meanings  of  words;  for  what  a  dictionary 
cannot  do,  and  what  comparison  does,  is  to  render 
the  meanings  of  words  appropriate  to  the  particular 
contexts  in  which  they  occur.  By  the  method  of 
comparison  we  find  the  relevant  meaning,  the  mean- 
ing that  is  required  by  the  universe  of  discourse 


170  A   TEXT-BOOK   OF  LOGIC 

within  which  our  thought  is  moving,  and  by  the 
purpose  which  controls  our  particular  assertions. 

Definition  per  genus  et  differentiam.  By  defini- 
tion, as  we  have  seen,  we  aim  to  substitute  definite- 
ness  for  indefiniteness  in  the  meaning  of  our  words, 
and  thus  to  avoid  ambiguities  of  statement.  We 
have  seen,  also,  that  not  all  cases  of  ambiguity  are 
overcome  best  by  definition,  but  only,  or  particularly, 
those  cases  in  which  the  vagueness  of  the  boundaries 
of  a  word's  meaning  obscures  the  sense  of  what 
we  wish  to  say.  In  definition,  therefore,  we  seek 
to  limit  the  range  of  a  word's  meaning,  by  giving 
an  appropriate  degree  of  definiteness  to  its  fringe 
or  outlying  area. 

Now  it  is  quite  obvious  that  we  cannot  limit 
the  meaning  of  our  words  in  the  way  required  by 
definition  if  these  words  are  used  or  understood  by 
us  with  no  meaning  at  all.  We  cannot  talk  about 
limiting  the  extent  of  our  words'  meanings  unless 
these  words  are  used,  and  are  understood,  in  some, 
however  vague,  sense.  Hence,  as  we  said  above, 
the  central  meaning  of  words  is  not  in  question  in 
these  cases  of  ambiguity ;  it  is  only  the  range  of  the 
word's  meaning  that  is  in  doubt.  It  would  seem, 
therefore,  that  the  limitations  that  we  put  upon 
our  meanings  in  defining  them  must  have  some  rela- 
tion to  these  meanings  themselves,  but  the  particular 
direction  in  which  the  limitation  is  made  depends 
upon  the  purpose  for  which  we  are  seeking  the  defi- 
nition. To  take  a  simpler  illustration,  if  the  purpose 
for  which  we  need  a  definition  of  'water'  is  domes- 


DEFINITION   AND   THE   PREDICABLES  171 

tic,  we  may  say  that  it  is  a  liquid  which  is  useful 
for  cleansing;  but  if  our  interests  are  chemical,  we 
must  say  that  the  liquid  is  composed  of  two  mole- 
cules of  hydrogen  and  one  of  oxygen.  In  both  in- 
stances, we  start  with  the  central  idea  of  water  as 
a  liquid,  and  in  both  we  limit  the  range  of  this 
meaning  in  a  direction  which  is  determined  by  the 
purpose  or  interest  that  the  definition  is  to  serve. 
It  would  seem,  consequently,  that  every  definition 
has  two  parts,  a  central  and  a  peripheral,  and  that 
these  are  different,  though  related,  aspects  of  a 
word's  explicit  meaning. 

Now  the  two  parts  of  which,  as  we  have  seen, 
the  meaning  of  words  is  comprised  are  called  in 
logic  the  genus  and  the  differentia  respectively.  By 
the  genus  we  mean  the  clear  centre,  and  by  the 
differentia  the  vague  periphery  of  a  word's  conno- 
tation. The  connection  between  the  two  is  obvious 
if  we  remember  that  both  are  specifications  of  a 
single  meaning.  Since,  therefore,  in  defining  a 
word's  meaning  we  start  with  the  recognition  of 
its  genus,  the  differentia  cannot  add  to  that  meaning 
anything  inconsistent  with  what  the  genus  already 
connotes.  That  is  to  say,  we  must  look  within  the 
range  of  meaning  broadly  marked  out  already  by 
its  genus  for  the  marks  that  make  the  meaning  of 
a  word  distinct.  The  differentia  must  lie  within  the 
genus,  and  not  outside  it,  if  we  are  to  mark  off  from 
encroaching  meanings  the  one  that,  by  definition, 
we  are  trying  to  make  distinct.  For  what  lies  out- 
side any  genus  belongs  to  another  genus,  or  is  that 


172  A   TEXT-BOOK   OF  LOGIC 

genus  itself,  and  is  not  likely  to  threaten  us  with 
ambiguity;  but  the  distinctions  that  lie  within  a 
genus  are  likely  to  be  overlooked  because  of  the  com- 
mon meaning  that  pervades  all  that  belongs  to  the 
genus.  For  example,  no  one  is  in  any  danger  of 
confusing  a  typewriter  with  the  table  on  which  it 
stands  because  each  belongs,  in  our  common  ac- 
quaintance with  it,  to  a  different  genus,  the  one  to 
the  genus  'objects  for  writing  with,'  and  the  other  to 
the  genus  'objects  for  placing  things  upon/  But  if, 
to  take  another  illustration,  the  poet  or  philosopher 
or  scientist  were  to  mistake  the  world  of  his  imagi- 
nation for  the  world  of  his  actual  experience,  this 
would  be  because  he  had  failed  to  observe  the  marks 
that  keep  the  two  worlds  distinct.  If,  again,  the 
student  were  to  use  the  words  'university*  and  'col- 
lege' synonymously,  this  would  be  because  he  had 
failed  to  notice,  within  the  meaning  that  both  have 
in  common,  the  specific  difference  by  which  the  one 
is  distinguished  from  the  other  in  the  same  genus. 
From  these  statements  and  illustrations  it  is  obvious 
not  only  how  genus  and  differentia  are  related  to 
each  other  in  a  logical  definition,  but  also  what  the 
terms  themselves  signify.  Thus,  by  a  genus  is  meant 
a  group  of  qualities  belonging  to  a  number  of  par- 
ticular objects  in  common.  The  word  is  also  used  to 
denote  any  group  of  objects  when  these  objects  are 
thought  of  as  possessing  common  qualities.  By  a 
differentia,  on  the  other  hand,  is  meant  the  specific 
difference  by  which  a  distinct  place  is  given  to  an 
object  within  a  genus  by  reason  of  its  possessing  a 


DEFINITION   AND   THE   PREDICABLES  173 

quality,  or  group  of  qualities,  that  does  not  belong 
to  any  other  member  of  its  genus.  Hence,  in  looking 
for  the  differentia  of  an  object  we  must  look  for  some 
quality,  or  group  of  qualities,  that  does  not  belong  to 
any  other  object  of  the  group  to  which  this  object 
belongs.  When  this  quality  or  group  of  qualities 
is  not  clearly  apprehended  we  are  liable  to  confuse 
one  thing  with  another. 

Verbal  and  Real  Definition.  The  distinction  be- 
tween real  and  verbal  definition,  or,  as  it  is  some- 
times stated,  between  scientific  and  nominal  defini- 
tion, is  as  old  as  Aristotle,  although  in  the  case  of 
verbal  definition  modern  writers  do  not  seem  agreed 
as  to  how  it  should  be  understood.  By  a  real  or 
scientific  definition  is  meant  a  definition  that  is  based 
upon  and  gives  a  description  of  the  essential  nature 
of  the  object  which  the  word  to  be  defined  denotes. 
Far  example,  a  'liquid'  is  defined  as  that  form  of 
matter  in  which  the  molecules  move  with  perfect 
freedom  without  changing  their  size.  Verbal  or 
nominal  definitions,  on  the  other  hand,  have  received 
at  least  two  different  interpretations.  The  first,  or 
Aristotelian,  interpretation  bids  us  regard  as  ver- 
bal definitions  the  current  or  popular  meanings  of 
words.  For  example,  the  definition  of  a  house  as  'a 
building  in  which  people  live'  would  be,  on  this  in- 
terpretation, a  verbal  definition.  The  second  inter- 
pretation would  make  any  definition  verbal  when 
the  word  in  question  is  used  to  indicate  what  any- 
thing is  called.  For  example,  the  definition  of  the 
word  'dog'  is  verbal  when  it  fails  to  convey  any 


174  A   TEXT-BOOK   OF   LOGIC 

information  about  the  essential  qualities  of  the  ob- 
ject that  the  word  denotes,  and  connotes  only  those 
qualities  which  make  the  use  of  the  word  appro- 
priate. 

Now  the  distinction  of  real  and  verbal  definition, 
and  the  variations  of  the  sense  in  which  verbal  defi- 
nitions are  understood,  are  interesting,  from  a  log- 
ical point  of  view,  because  they  raise  the  question 
whether  in  definition  we  are  dealing  with  thoughts 
or  things,  with  the  nature  of  objects,  or  with  our 
interests  and  purposes  in  their  relation  to  objects. 
According  to  the  view  of  logic  which  we  are  ex- 
pounding, no  answer  can  be  given  to  this  question 
which  ignores  the  intimate  connection  of  thoughts 
and  things.  In  the  pursuit  of  knowledge,  we  are  not 
interested  exclusively  in  either  thoughts  or  things; 
knowledge,  as  we  have  shown,  exists  in  the  form 
of  thoughts-about-things.  If  this  is  borne  in  mind, 
it  will  be  evident  that  in  all  our  efforts  to  avoid 
ambiguity  we  strive  to  bring  our  thoughts  into  rela- 
tion with  things,  and  things  into  relation  with 
thoughts;  and  in  definition  it  is  sometimes  the  one 
and  sometimes  the  other  of  these  factors  of  knowl- 
edge that  requires  to  be  made  explicit.  In  the  light 
of  this  statement,  the  distinction  of  verbal  and  real 
definition  is  not  an  absolute  but  a  relative  one,  and 
were  it  not  for  the  fact  that  our  words  need  to  be 
wedded  to  fixed  meanings,  and  meanings  to  be  fixed 
and  made  definite  by  the  use  of  words,  the  distinc- 
tion would  have  no  particular  logical  interest,  and 
might  vanish  entirely.  The  distinction,  however, 


DEFINITION   AND   THE   PREDICABLES  175 

persists  and  is  likely  to  persist,  because  our  knowl- 
edge is  always  in  different  stages  of  development, 
and  because  with  the  improvement  of  knowledge 
old  words  receive  more  precise  meanings,  and  new 
terms  are  constantly  taking  their  place  in  the  vocab- 
ulary of  the  people.  But  while  this  is  true,  it  is 
quite  clear  that  the  goal  toward  which  we  move  in 
definition  is  a  truer  insight  into  reality,  and  the 
preservation  of  this  insight  in  terms  that  adequately 
express  it. 

The  Relation  of  Purpose  to  Definition.  We  have 
said  that  the  aim  of  every  definition  is  to  make  our 
knowledge  of  things  more  precise,  and  to  fix  this 
knowledge  in  words.  So  far  as  this  is  true,  we  are 
emphasising  the  relation  of  definition  to  the  objects 
of  our  knowledge.  But  what  objects  and  what  fea- 
tures of  objects  are  of  importance  for  knowledge, 
depends  upon  the  purpose  for  which  the  definition 
of  these  objects  is  sought.  A  change  in  purpose  is 
liable  to  produce  a  corresponding  change  in  the  defi- 
nition. For  example,  if  my  purpose  is  to  ascertain 
the  structural  character  of  a  circle,  my  definition 
will  call  attention  to  the  fact  that  a  circle  is  a  plane 
figure  bounded  in  such  a  way  that  all  straight  lines 
drawn  from  a  fixed  point,  called  the  centre,  to  this 
bounding  line  are  of  equal  length.  If,  on  the  other 
hand,  my  purpose  is  to  enable  one  to  draw  a  circle, 
it  will  then  be  defined  as  the  plane  figure  described 
by  a  point  moving  at  a  given  distance  around  an- 
other fixed  point.  This  is  called,  in  contrast  to  the 
structural,  a  genetic  definition.  It  should  be  ob- 


176  A   TEXT-BOOK   OF  LOGIC 

served  that  the  distinction  between  structural  and 
genetic  definition  is  not  confined  to  mathematics; 
the  distinction,  that  is,  does  not  depend  on  the  sub- 
ject matter,  but  upon  the  purpose  for  which  the 
definition  is  sought.  But  every  case  of  definition 
whether  structural  or  genetic  is  per  genus  et  differ- 
entiam,  a  form  of  definition  which  we  must  take  as 
typical  of  all  definition  whatsoever. 

Tests  of  a  Definition.  In  text-books  of  logic,  it 
is  customary  to  enumerate  a  number  of  other  rules 
of  definition  than  the  one  to  which  our  attention  has 
been  exclusively  directed.  There  results  from  this 
mode  of  presenting  the  subject  an  impression  of 
complexity  and  difficulty  that  is  really  foreign  to  it, 
and  the  student  is  deprived  of  the  incentive  that 
comes  from  a  simple  and  unencumbered  statement 
to  make  a  practical  use  of  that  rule.  We,  therefore, 
emphasise  again  the  fact  that  all  definition  is  to  be 
sought  per  genus  et  differentiam,  and  that  this  rule, 
when  properly  applied,  relieves  of  ambiguity  any 
statement  that  is  caused  by  indefiniteness  in  the 
meaning  of  words,  and  that  it  is  the  only  one  where- 
by this  result  can  be  accomplished. 

The  only  question  remaining  on  our  hands  is, 
then,  how  we  are  to  know  whether  the  rule  has  been 
properly  applied.  It  is  as  an  answer  to  this  ques- 
tion that  the  other  so-called  rules  have  their  value; 
and  because  they  provide  us  with  an  answer  to  this 
question  they  are  not  rules  of  definition  at  all,  but 
tests  of  the  accuracy  of  definitions  reached  in  some 
other  way.  We  shall  consider  them  in  this  light  in 


DEFINITION   AND   THE   PREDICABLES  177 

the  following  paragraphs,   and  thereby  make  the 
one  rule  of  definition  itself  more  definite. 

In  the  first  place,  let  us  recall  the  fact  that  the 
object  of  definition  is  to  limit  the  extent  of  a  word's 
meaning,  and  in  limiting  it  to  make  it  more  exact. 
Omnis  determinatio  limitatio  est:  we  make  our 
knowledge  of  objects  definite  by  limiting  the  range 
of  the  object's  nature  of  which  our  knowledge,  at 
any  time,  takes  account.  Nowhere  more  than  in  the 
intellectual  life  does  the  proverb  'grasp  all  lose  all' 
have  a  more  pertinent  application.  Only  if  we  are 
willing  to  let  some  things  go,  can  we  gain  anything 
at  all.  But  in  order  to  gain  something,  we  must 
systematically  eliminate  what  does  not  have  a  bear- 
ing upon  the  purpose  for  which  knowledge  is  being 
sought.  And,  as  we  have  shown,  definition  is  a 
means  of  systematically  eliminating  encroaching 
meanings  which  are  threatening  the  definiteness  of 
our  assertions.  It  would  seem,  therefore,  that  one 
of  the  dangers  to  which  our  definitions  may  be  ex- 
posed is  to  be  found  in  their  particular  range:  our 
definitions  may  be  either  too  broad  or  too  narrow. 
We  shall  examine  each  of  these  cases  separately. 

If  the  genius  of  a  definition  is  not  proximate  our 
definition  is  likely  to  be  too  broad.  For  example,  if 
we  define  a  square  as  a  quadrilateral  figure  (genus) 
whose  angles  are  right-angles  (differentia),  it  is 
obvious  that  we  are  in  danger  of  confusing  a  square 
with  an  oblong  which  is  also  a  quadrilateral  rec- 
tangular figure.  The  definition  is  too  wide.  To 

12 


178  A   TEXT-BOOK   OF   LOGIC 

rectify  the  definition  we  shall  have  to  compare  the 
square  with  an  oblong,  and  then  we  shall  observe 
that  while  both  are  quadrilateral,  this  is  not  their 
nearest  genus,  that  is,  it  does  not  contain  all  the 
qualities  that  they  have  in  common.  Besides  being 
quadrilateral  they  are  both  rectangular.  The  class, 
therefore,  to  which  they  both  belong  is  quadrilateral 
rectangle.  Now,  within  this  class,  the  differentia 
of  the  square  will  be  equilateral,  having  all  its  sides 
equal.  Our  finished  definition  of  a  square  will, 
therefore,  be  'a  quadrilateral  rectangle  having  all  its 
sides  equal/ 

If  the  differentia  of  a  definition  is  not  exact  our 
definition  is  likely  to  be  too  narrow.  By  the  differ- 
entia being  exact  we  mean  that  it  must  be  such  that 
only  the  objects  denoted  by  the  term  we  are  defining 
possess  the  attribute  in  question.  Suppose  we  were 
to  define  man  as  a  civilised  animal,  the  differentia 
'civilised'  would  not  be  exact,  and  the  definition  too 
narrow,  because  it  excluded  from  the  class,  man, 
all  individuals  who  had  not  reached  a  certain  stage 
of  culture.  To  test  the  accuracy  of  our  differentia 
we  may  ask  ourselves  the  question :  Do  all  and  only 
the  objects  denoted  by  the  term  we  are  defining 
possess  the  quality  connoted  by  the  differentia  by 
means  of  which  we  are  seeking  to  mark  off  the 
meaning  of  the  term  from  that  of  other  closely 
related  terms?  If  not,  the  definition  will  be  too 
narrow. 

After  we  have  done  the  best  we  can  to  secure 
the  accuracy  of  our  definition  in  the  ways  mentioned, 


DEFINITION  AND  THE   PREDICABLES  179 

we  may  then  examine  the  definition  as  a  whole.  We 
can  do  this  if  we  remember  that  a  true  definition 
can  always  be  simply  converted.  If  it  is  true,  for 
example,  that  'a  house-dog  is  a  domestic  animal  that 
barks/  then,  if  our  definition  is  accurate,  it  must  be 
true  that  'a  domestic  animal  that  barks  is  a  house- 
dog/ That  is  to  say,  the  object  defined  (the  defini- 
endum)  and  the  definition  must  be  commensurate. 
Or,  to  state  the  same  fact  another  way,  whatever 
can  be  relevantly  predicated  of  the  object  defined 
must  be  predicable  of  the  definition,  and  vice-versa. 
This  rule  guards  against  anything  superfluous  in 
definition. 

Further,  the  terms  of  the  definition  must  be  of 
the  same  order  as  the  term  defined.  If,  for  example, 
we  defined  the  body  as  'the  visible  garment  of  the 
soul/  it  is  obvious  that  the  word  soul  belongs  to  the 
order  of  spiritual  facts,  and  is  transferred  to  the 
physical  order,  the  order  of  the  term  defined.  The 
uselessness  of  definitions  of  this  kind  may  be  over- 
come if  we  take  our  clue  to  the  order  of  the  terms 
in  which  our  definition  must  be  stated  from  the 
order  of  the  term  to  be  defined.  Hence,  to  satisfy 
this  requirement,  we  may  ask  ourselves  the  ques- 
tion :  Are  all  the  terms  of  the  definition  homo- 
geneous with  the  term  defined?  In  this  way  we 
avoid  the  indefiniteness  that  arises  from  the  use  of 
figurative  language. 

Another  requirement  of  a  good  definition  is  that 
the  terms  of  the  definition  should  be  more  ele- 
mentary than  the  term  defined.  The  elementariness 


180  A  TEXT-BOOK   OF  LOGIC 

of  a  term  is  determined  with  reference  to  the  uni- 
verse within  which  the  term  to  be  defined  belongs. 
For  example,  the  terms  'rational'  and  'animal'  are 
more  elementary  than  the  term  'man'  of  which  they 
are  predicated  as  the  definition;  and  in  the  same 
way  the  terms  'mammal'  and  'living  in  the  ocean' 
are  more  elementary  than  the  term  'whale.'  By  ele- 
mentary, that  is,  is  meant  elementary  in  the  field 
of  knowledge  to  which  the  term  to  be  defined  re- 
fers, and  not  to  the  range  of  information  that  may 
at  any  time  be  current.  Hence,  for  one  who  has  no 
acquaintance  with  the  field  of  knowledge  with  which 
the  term  is  connected,  we  may  remove  the  ambi- 
guity that  exists  in  the  meaning  of  the  term  better 
by  pointing  out  a  specimen  of  the  class  or  kind  of 
thing  that  the  term  denotes  than  we  can  by  a 
definition. 

Again,  a  term  must  not  be  defined  by  the  use 
of  the  term  itself  or  by  one  of  its  synonyms.  If 
this  occurs  we  have  what  is  called  a  circular  defini- 
tion. For  example,  if  we  define  a  power  as  'a  force 
that  tends  to  produce  motion,'  we  are  obviously 
guilty  of  a  breach  of  this  requirement  since  the  word 
force  has  the  same  meaning  as  the  word  to  be  de- 
fined. 

Finally,  the  form  of  our  definition  must  be  pos- 
itive if  the  term  to  be  defined  is  positive,  and  neg- 
ative if  the  term  to  be  defined  is  negative.  For 
example,  the  term  'gentleman'  has  a  positive  mean- 
ing, and,  therefore,  it  would  be  a  breach  of  this 
requirement  if  we  were  to  define  it  as  'a  man  who 


DEFINITION   AND   THE   PREDICABLES  181 

has  no  definite  means  of  support.'  But  if  we  were 
to  define  an  alien  as  'a  man  who  is  not  a  citizen  of 
the  country  with  respect  to  which  he  is  declared  an 
alien,'  we  should  satisfy  the  requirement,  because 
the  term  alien  carries  with  it  a  negative  meaning. 
The  Problem  and  Classification  of  the  Predicables. 
Whatever  can  be  predicated  of  a  subject  is  called 
a  predicable.  Now  if  we  ask  ourselves  the  ques- 
tion, What  sort  of  things  can  be  predicables,  i.  e., 
can  be  predicated  of  a  subject?  we  have  definitely 
placed  before  ourselves  an  inquiry  that  engaged  the 
attention  of  Aristotle,  and  again  of  Porphyry  six 
hundred  years  after  Aristotle's  time.  The  answers 
that  Aristotle  and  Porphyry  gave  to  this  question 
may  be  placed  in  two  separate  columns  thus : 

ARISTOTLE'S  LIST  OP  PORPHYRY'S  LIST  OF 

PREDICABLES  PREDICABLES 

Definition  Genus 

Genus  Species 

Differentia  /  Differentia 

Proprium  Proprium 

Accident  Accident 

The  various  kinds  of  things  that  can  form  the  pred- 
icates of  logical  propositions  are  the  kinds  of  things 
indicated  by  the  names  in  these  two  lists. 

An  examination  of  these  lists  will  show  that  they 
differ  in  the  substitution  by  Porphyry  of  'species' 
for  Aristotle's  'definition/  the  other  four  predi- 
cables being  the  same.  But  although  apparently 
only  a  slight  difference,  this  change  indicates  a  dif- 


182  *A  TEXT-BOOK  OF  LOGIC 

ference  in  the  doctrine  of  definition  of  sufficient  sig- 
nificance to  demand  a  word  or  two  of  explanation. 
The  significance  of  this  difference  in  the  two  lists 
can,  perhaps,  be  seen  if  we  remark  that  the  question, 
What  sorts  of  thing  can  be  predicated?  is  not  un- 
connected with  the  question,  What  kinds  of  thing 
can  be  defined?  We  have  seen,  for  example,  that 
in  logical  propositions  we  are  concerned  with  both 
subject  and  predicate  terms,  and  it  has  been  made 
clear  that  our  predicate  terms  must  not  only  be 
predicable,  but  predicable  of  the  objects  denoted  by 
our  subject  terms.  If,  for  example,  there  should  be 
anything  indefinable,  such  a  thing  would  correspond 
to  what  is  called  an  individual ;  and  of  such  individ- 
ual it  is  obvious  that  we  cannot  affirm  a  genus  and 
a  differentia.  Now,  it  is  the  difference  between  the 
views  of  Aristotle  and  Porphyry  as  to  the  kinds  of 
thing  that  are  capable  of  definition  that  accounts  for 
the  difference  in  their  lists  of  predicables.  Aristotle 
held  that  it  is  only  as  a  universal  or  species  that 
anything  could  be  defined.  Porphyry  held  that  the 
subject  of  predication  might  be  not  only  a  species, 
but  also  an  individual.  It  was,  therefore,  reason- 
able to  include  species  in  his  list  of  predicables,  for, 
doubtless,  its  species  can  be  predicated  of  an  indi- 
vidual ;  but  it  would  have  been  a  mere  tautology  to 
predicate  species  of  itself  as  would  have  happened 
if  this  predicable  had  been  included  in  Aristotle's 
list. 

Our  exposition  of  the  doctrine  of  the  predicables 
will  follow  in  the  main  the  Aristotelian  view.    We 


DEFINITION   AND   THE   PREDICABLES  183 

shall  assume  that  the  subject  terms  of  logical  prop- 
ositions denote  objects,  or  groups  of  objects,  that 
are  thought  of  as  possessing  attributes  which  ex- 
press the  common  nature  of  all  the  objects  to  which 
the  subject  term  can  be  applied.  Now  if  it  is  asked 
what  can  be  predicated  of  objects  so  conceived,  the 
answer  is  given  in  the  list  of  Aristotelian  predi- 
cables.  Before,  however,  we  consider  in  detail  what 
each  of  these  predicables  means,  we  may  point  out 
that  they  are  not  all  related  to  a  subject  in  exactly 
the  same  way.  Some  of  the  predicables  are  com- 
mensurate with  their  subjects,  and  some  are  non- 
commensurate.  To  the  former  class  belong  defini- 
tion and  proprium;  to  the  latter,  genus,  differentia, 
and  accident. 

The  Commensurable  Predicables.  By  a  commen- 
surate predicable  is  meant  one  that  is  found  wher- 
ever the  subject  of  which  it  is  predicated  is  found. 
It  is  an  attribute,  or  group  of  attributes,  that  is 
always  present  when  the  object  is  present,  and  ab- 
sent when  the  object  is  absent.  This  class  of  pred- 
icables we  shall  explain  briefly  in  this  section. 

The  definition  we  have  considered  already.  It  is, 
as  we  have  seen,  an  answer  to  the  question,  What 
is  it?  and  this  question  may  be  asked  of  anything, 
of  an  attribute  as  well  as  of  a  substance.  For  ex- 
ample, if  we  ask  what  acceleration  is,  and  the  phy- 
sicist were  to  answer,  change  of  velocity  per  second, 
he  is  offering  this  as  a  definition,  that  is,  a  state- 
ment of  what  it  is  that  makes  anything  the  kind 
of  thing  called  acceleration.  Similarly,  when  an 


184  A  TEXT-BOOK   OF  LOGIC 

organism  is  defined  as  a  material  body  of  which  the 
parts  are  reciprocally  related  as  ends  and  means, 
we  should  refuse  to  recognize  as  an  organism  any 
object  which  did  not  manifest  these  particular  char- 
acteristics. The  propositions,  therefore,  in  which 
the  predicate  terms  claim  to  be  definitions  are  those 
in  which  the  predicates  also  claim  to  be  commensu- 
rate with  their  subject  terms.  This  is  only  another 
way  of  saying,  as  we  said  above,  that  the  state- 
ments which  embody  definitions  must  be  capable  of 
simple  conversion.  The  definition  states  what  is 
essential  to  the  existence  of  the  objects  denoted  by 
the  term  that  is  defined. 

A  proprium  or  property  is  an  attribute  peculiar 
to  or  characteristic  of  an  object,  and  is  commen- 
surate with  its  existence,  but  it  is  not  an  essential 
part  of  its  definition.  We  may  state  the  relation 
between  the  proprium  and  definition  by  saying  that 
by  means  of  the  proprium  we  develop  the  meaning 
of  a  term  from  the  point  at  which  its  definition 
stopped.  From  this  it  will  be  obvious  that  whether 
we  go  beyond  the  meaning  that  is  assigned  to  a 
term  in  its  definition  will  depend  upon  a  motive 
other  than  that  which  makes  definition  necessary. 
In  other  words,  the  propria  of  terms  are  those  char- 
acteristic features  of  an  object's  nature  which  re- 
main after  definition  has  removed  any  existing  am- 
biguity; and  whether  these  are  predicated  as  part 
of  the  term's  meaning  will  depend  upon  whether 
special  motives  operate  to  make  them  explicit.  For 
example,  an  equilateral  triangle  may  be  defined  as 


DEFINITION   AND   THE   PREDICABLES  185 

a  three-sided  plane  figure  having  all  its  sides  equal. 
This  statement  is  sufficient  for  the  purpose  of  dis- 
tinguishing this  kind  of  triangle  from  all  other 
kinds.  But  if  we  were  interested  further  in  equi- 
lateral triangles,  we  should  find  that  they  are  also 
equiangular,  and  this  fact  of  being  equiangular  is 
called  a  property  of  the  kind  of  triangles  in  ques- 
tion. Likewise,  contractility,  irritability,  assimilat- 
ing food,  reproduction  after  its  kind,  are  properties 
of  an  organism  as  this  term  was  defined  above. 

The  Non-Commensurable  Predicables.  By  a  non- 
commensurate  predicable  is  meant  any  quality  which 
alone  does  not  exhaust  the  nature  of  an  object,  or 
which  belongs  to  an  object  in  some  only  of  the  ob- 
ject's relations.  In  neither  case  is  the  nature  of 
the  objects  denoted  by  the  term  made  entirely  ex- 
plicit. The  following  illustrations  will  make  this 
clear. 

We  may,  in  the  first  place,  predicate  of  any  sub- 
ject the  genus  to  which  it  belongs.  That  is  to  say, 
we  may  affirm  the  area  of  clear  meaning  of  a  term, 
and  this  may  be  all  that  is  necessary  to  convey  our 
meaning.  It  is  obvious  that  we  are  here  dealing  with 
the  class  of  cases  that  were  considered  above  under 
the  head  of  translation.  But,  as  we  saw  there,  the 
genus  alone  does  not  tell  us  all  that  is  necessary 
for  a  complete  understanding  of  any  object's  nature. 
The  genus  is,  therefore,  an  incommensurable  pred- 
icable. We  may,  in  the  second  place,  predicate  of 
a  subject  its  differentia,  that  is,  that  part  of  the  es- 
sential nature  of  the  subject  which  distinguishes  it 


186  A  TEXT-BOOK  OF  LOGIC 

from  other  species  of  the  same  genus.  If,  therefore, 
we  are  in  danger  of  ambiguity  from  a  tendency  to 
confuse  species,  we  may,  to  make  our  meaning  clear, 
resort  to  the  method  of  calling  attention  to  the 
specific  differences  of  the  objects  that  we  have  hith- 
erto failed  to  distinguish.  But  the  differentia  alone, 
as  we  have  seen,  does  not  exhaust  the  nature  of  any 
object,  and  it  is  not,  therefore,  a  commensurable 
predicable.  In  the  third  place,  we  may  predicate 
some  attribute  not  included  in  the  definition  of  a 
subject,  that  is  to  say,  an  attribute  that  may  or  may 
not  belong  to  the  subject.  For  example,  there  is 
nothing  in  the  nature  of  a  pen  that  it  should  be 
made  by  a  particular  firm,  or  that  it  should  belong 
to  a  particular  person.  These  are  accidental  rela- 
tions, and  belong  to  the  pen  merely  as  an  individual. 
All  such  attributes,  not  contained  in  the  definition 
or  proprium,  are  called  accidents. 

REFERENCES 

H.  A.  Aikins,  The  Principles  of  Logic,  Ch.  II.,  III. 

J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Pt.  I., 
Ch.  V. 

J.  G.  Hibben,  Logic  Deductive  and  Inductive,  Chs.  IV.,  V. 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Lesson  XII. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  V. 

W.  Minto,  Logic  Inductive  and  Deductive,  Pt.  II.,  Chs.  I.,  II. 

C.  Read,  Logic  Deductive  and  Inductive,  3d  Edition,  Ch. 
XXII. 

W.  J.  Taylor,  Elementary  Logic,  Chs.  III.,  VI. 


DEFINITION  AND   THE   PREDICABLES  187 


ADVANCED 

R.  W.  B.  Gibson,  The  Problem  of  Logic,  Chs.  II.,  III. 

H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Chs.  IV.,  V. 

H.  Lotze,  Logic,  Bk.  II.,  Ch.  I. 

J.  S.  Mill,  A  System  of  Logic,  Bk.  I.,  Chs.  VII.,  VIII. 

F.  C.  S.  Schiller,  Formal  Logic,  Chs.  V.,  VI. 

C.  Sigwart,  Logic,  Pt.  II.,  §§  44. 

J.  Venn,  Empirical  Logic,  Ch.  XI. 

J.  Welton,  A  Manual  of  Logic,  Vol.  I.,  Bk.  I.,  Chs.  III.,  V. 


QUESTIONS 

1.  From  what  two  standpoints  may  the  logical  discussion 
of  terms  be  carried  on,  and  to  what  new  problems  does 
such  a  discussion  give  rise? 

2.  Define  each  of  the  problems  enumerated  in  your  answer 
to  the  previous  question. 

3.  Define  the  nature  and  limits  of  the  demand  for  non- 
ambiguous  statements. 

4.  What  is  the  practical  importance  of  being  able  to  make 
non-ambiguous  statements? 

5.  State  and  criticise  the  traditional  doctrine  of  ambiguity. 

6.  In  what  sense  can  ambiguity  be  said  to  be  the  funda- 
mental problem  of  logic? 

7.  Explain  the  nature  of  translation  as  a  method  of  over- 
coming .ambiguity. 

8.  What  conditions  call  for  the  employment  of  translation 
in  the  removal  of  ambiguity? 

9.  What  conditions  call  for  the  employment  of  definition  in 
the  removal  of  ambiguity? 

10.  Explain   and   illustrate:      The  method   of  definition   is 
comparison. 

11.  What  is  meant  by:    Logical  definition  is  per  genus  et 
differentiam? 


188  A  TEXT-BOOK   OF  LOGIC 

12.  What  do  you  understand  by  real  and  verbal  definition? 
In  what  two  senses  may  verbal  definition  be  understood? 

13.  What  is  the  logical   significance   of  the   distinction  of 
real  and  verbal  definition? 

14.  What  is  the  relation  of  purpose  to  logical  definition? 

15.  In   what  two  ways   may   our  definitions   fall   short   of 
being    strictly    accurate? 

16.  Explain  and  illustrate  how  a  definition  may  be  too  broad. 

17.  Explain  and  illustrate  how  a  definition  may  be  too  nar- 
row. 

18.  How  does  the  simple  conversion  of  a  definition  guard 
against  introducing  anything  superfluous  into  the  defi- 
nition? 

19.  How  may  we  guard  against  figurative  language  in  defi- 
nitions? 

20.  Explain:      The  terms   of   a   definition   should   be   more 
elementary  than  the  term  to  be  defined. 

21.  What  is  meant  by  a  circular  definition,  and  how  may 
circular  definitions  be  avoided? 

22.  What  do  you  understand  by  a  predicable? 

23.  How  many  predicables  are  there,  and  what  is  the  dif- 
ference between  Aristotle's  and  Porphyry's  lists  of  the 
predicables? 

24.  What  is  the  relation  of  the  problem  of  the  predicables 
to  that  of  definition? 

25.  Explain   why   Aristotle's    and    Porphyry's    lists   of   the 
predicables  differ? 

26.  What  is  meant  by  a  commensurable  predicable? 

27.  Which  of  the  predicables  are  commensurable? 

28.  In  what  sense  is  a  definition  a  predicable? 

29.  What  is  a  proprium? 

30.  What  is  meant  by  a  non-commensurable  predicable? 

31.  Explain   genus,   differentia,   and   accident   as    non-com- 
mensurable predicables. 


DEFINITION  AND  THE  PREDICABLES  189 


EXERCISES 

1.  Write  three  ambiguous  statements  whose  ambiguity  can 
be  removed  by  translation. 

2.  Write  three  ambiguous  statements  whose  ambiguity  can 
be  removed  by  definition. 

3.  Define,  and   state,  in  each  case,  the  purpose  that  the 
definition  is  intended  to  serve:   anger,  river,  house,  em- 
peror, metal,  justice. 

4.  Criticise  the  following  definitions,  and  show  what  rules, 
if  any,  are  violated  by  them: 

(1)  Thunderbolts   are  the  winged   messengers   of  the 
gods. 

(2)  Round   is   a   quality  that  belongs   to   any  rotund 
object. 

(3)  Man  is  a  vertebrate  animal. 

(4)  An  inflammation  is   some  abnormal   condition   of 
one  of  the  body  tissues. 

(5)  An  absentee  is  a  person  who  does  not  live  in  his 
own  country,  or  who  does  not  look  after  his  own 
property. 

(6)  Prudence  is  the  ballast  of  the  moral  vessel. 

5.  Construct  three  definitions  for  the  purpose  of  showing 
how  definition  depends  upon  comparison. 

6.  To  which  of  the  Predicables  does  each  of  the  following 
predicates   belong : 

(1)  The  whale  is  a  mammal. 

(2)  The  whale  is  a  vertebrate. 

(3)  The  whale  lives  in  the  ocean. 

(4)  The  whale  was  caught  and  brought  to  land. 

(5)  Logic  is  a  good  mental  discipline. 

(6)  The  tiger  is  a  predatory  animal. 

(7)  Englishmen  are  keen  sportsmen. 

(8)  Lord  Shaftesbury  was  a  great  philanthropist. 

7.  Give  the  genus,  differentia,  proprium,  and  accidens  of 
(a)   peninsula,   (b)   triangle,   (c)   affirmative  statement, 


CHAPTER  VII 
DIVISION  AND  CLASSIFICATION 

Relation  of  Definition  and  Division.  Whenever 
ambiguity  threatens  any  statement  on  account  of 
the  vagueness  of  the  outlying  range  of  a  word's 
meaning,  we  may  remove  the  ambiguity  by  defining 
the  word's  meaning.  The  method  of  definition,  as 
we  saw  in  the  last  chapter,  is  comparison.  By  this 
method  we  distinguish  a  meaning  from  one  or  more 
others  with  which  we  are  in  danger  of  confusing  it, 
and  our  result  is  a  division  of  the  genus  into  two 
or  more  species.  There  is,  however,  nothing  in  the 
nature  or  conditions  of  definition  that,  in  principle, 
assures  us  that  all  the  distinguishable  meanings  of 
a  genus  have  been  discovered,  and  nothing,  there- 
fore, that  assures  us  that  we  have  examined  all  the 
species  which  belong  to  the  genus  from  which  our 
definition  starts.  If,  therefore,  instead  of  asking 
how  one  species  differs  from  another,  we  wished  to 
know  how  many  species  there  are  in  a  given  genus, 
we  should  be  confronted  with  a  new  problem  which 
it  is  the  business  of  logical  division  to  consider;  for 
by  division  we  mean,  in  general,  the  method  that 
must  be  employed  to  develop  systematically  all  the 
species  which  belong  to  a  genus.  Now,  if  it  is  asked 
why  any  one  should  raise  such  a  question  as  this,  we 
can  only  say  that  the  demand  for  non-ambiguous 
statements  may  be  left  unsatisfied  after  making  the 

(190) 


DIVISION   AND   CLASSIFICATION  191 

meaning  of  our  words  as  clear  as  possible.  Ambi- 
guity, in  other  words,  may  be  occasioned  not  only 
by  uncertainty  in  the  connotation  of  terms,  but  also 
by  uncertainty  in  their  denotation;  and  whenever 
there  is  vagueness  in  either  respect  there  is  likely 
to  be  a  corresponding  vagueness  in  the  other.  From 
this  point  of  view,  logical  definition  and  division  are 
closely  connected  problems,  and  they  differ  merely 
as  one  stage  differs  from  another  in  a  single  process. 
In  logical  division  we  carry  further  the  process  that 
begins  in  logical  definition,  and  the  object  is  to  re- 
move any  remaining  uncertainty  in  a  word's  mean- 
ing. 

What  is  Meant  by  Logical  Division.  The  word 
'division'  is  not  well  chosen  to  designate  the  process 
that  we  have  now  to  describe.  If  it  should  suggest, 
as  it  ordinarily  must,  that  it  is  the  method  by  which 
we  split  up  a  genus  into  its  component  parts,  in 
much  the  same  way  that  a  house-wrecker  separates 
the  doors,  windows,  joists,  etc.,  of  the  building  he 
is  dismantling,  we  should  be  misled  entirely  in  our 
understanding  of  what  the  term  means  or  the  proc- 
ess implies.  If  this  were  the  sense  in  which  we  were 
required  to  understand  the  word,  its  application 
would  not  give  us  a  clearer  apprehension  of  a  term's 
meaning,  but  would  result  in  the  destruction  of  the 
meaning  altogether.  It  will,  perhaps,  set  the  mat- 
ter in  a  clearer  light  if  we  say  that  logical  division, 
like  logical  definition,  starts  with  species  or  con- 
cepts, and  that  in  both  cases  we  are  concerned  with 
the  kinds  in  which  the  species  is  found  realised. 


192  A  TEXT-BOOK   OF  LOGIC 

This  being  the  case,  we  cannot  say  that  a  genus  is 
the  sum  of  its  species;  we  can  only  say  that  it  is 
differentiated  into  its  species. 

In  logical  division,  we  are  concerned  with  the 
relation  of  a  genus  and  its  species.  But  that  rela- 
tion, as  we  have  just  seen,  cannot  be  one  of  a  whole 
to  its  parts;  it  is  rather  a  relation  in  which  the 
species  disjunctively  enumerate  the  alternatives 
which,  when  taken  as  an  enumeration,  denote  the 
range  of  a  term's  meaning.  That  is,  by  division  we 
analyse  the  denotation  of  a  term's  meaning.  For 
example,  if  we  should  divide  the  genus  'rectangle' 
into  two  species,  one  with  its  adjacent  sides  equal, 
and  the  other  with  its  adjacent  sides  unequal,  we 
cannot  mean  by  rectangle,  in  such  a  case,  the  sum 
of  these  two  species.  'Rectangle'  does  not  mean  the 
square  plus  the  oblong;  it  means  either  the  square 
or  the  oblong.  That  is  to  say,  the  genus  is  realised 
in  each  of  its  species ;  the  species  of  any  genus  ex- 
hibit distributively,  not  collectively,  a  word's  mean- 
ing. 

If,  now,  we  should  seek  to  derive  from  these 
statements  about  the  nature  of  logical  division  a 
rule  which,  when  applied  to  any  case,  will  serve  as 
a  test  of  the  accuracy  with  which  the  division  has 
been  carried  out,  we  may  perhaps  say  that  we  must 
be  able  to  predicate  the  genus,  or  whole  that  is  di- 
vided, of  each  of  the  species  of  a  logical  division. 
Thus,  in  the  previous  example,  we  called  the  oblong 
a  rectangle,  and  also  the  square  a  rectangle.  Each 
js  the  whole  of  what  a  rectangle  is.  To  take  another 


DIVISION  AND  CLASSIFICATION  193 

illustration.  The  genus  'human  being'  may  be  log- 
ically divided  into  'man,'  'woman,'  etc.,  and  the  genus 
-human  being  —  of  which  they  are  the  species, 
may  be  predicated  of  each  one,  thus :  'a  man  is  a 
human  being,'  'a  woman  is  a  human  being,'  etc. 

In  this  discussion  of  the  nature  of  logical  divi- 
sion we  have  seen  (1)  that  logical  division  is  the 
process  by  which  the  range  of  a  term's  meaning 
can  be  exhaustively  determined.  It  follows  from 
this  that  the  process  of  logical  division  can  be  ap- 
plied only  to  what  is  in  its  nature  general,  in  other 
words,  to  a  species  or  concept.  The  genus,  species, 
or  concept  to  which  the  process  of  division  is  applied 
is  called  the  totum  divisum.  We  have  seen  also  (2) 
that  the  sub-species  of  the  whole  that  is  divided 
enumerate  disjunctively  the  kinds  into  which  the 
whole  is  differentiated,  that  they  are  not  the  parts 
which  when  taken  together  constitute  the  whole. 
From  this  it  follows  (3)  that  we  must  be  able  to 
predicate  of  each  kind  the  qualities  connoted  by  the 
genus  or  whole  that  is  divided.  When  this  is  not 
possible  logical  division  has  not  taken  place. 

Other  Kinds  of  Division.  It  will  help  to  keep  the 
meaning  of  logical  division  distinct,  if  we  describe 
the  characteristics  of  other  operations  that  go  by 
the  same  general  name  of  division.  Of  these,  there 
are  in  particular  three :  metaphysical,  physical,  and 
verbal  division.  These  are,  like  logical  division, 
mental  operations,  but  each  serves  a  distinct  pur- 
pose. The  purpose  of  logical  division,  as  we  have 

13 


194  A  TEXT-BOOK   OF  LOGIC 

seen,  is  to  enumerate  the  kinds  or  species  into 
which  a  genus  is  differentiated,  or,  what  is  the  same 
thing,  the  kinds  or  species  in  which  the  qualities  of 
the  genus  are  realised.  The  purpose  of  metaphysical 
division  is  to  distinguish  the  several  attributes 
which  are  capable  of  being  predicated  of  a  genus. 
This  kind  of  division  obviously  lies  at  the  founda- 
tion of  the  problem  of  the  predicables  which  was 
considered  in  the  last  chapter.  For  the  problem  of 
the  predicables,  as  we  saw,  was  concerned  with  the 
character  of  the  attributes  that  could  be  predicated 
of  any  species.  When,  therefore,  we  divide  a  spe- 
cies into  its  genus,  differentia,  proprium  and  acci- 
dens,  we  are  not  employing  what  is  technically 
known  as  logical  division,  but  a  method  that  is 
known  as  metaphysical  division.  The  difference 
between  these  two  methods  may  be  brought  out  in 
the  statement  that  in  metaphysical  division  we 
must  be  able  to  predicate  of  the  genus  the  species 
which  our  division  has  been  the  means  of  distin- 
guishing; whereas  in  logical  division  the  converse 
statement  holds  true,  that  is,  it  is  the  genus  which 
must  be  predicable  of  the  species.  For  example,  if 
we  divide  'organism'  into  'animals/  'birds/  'fishes' 
and  'reptiles/  we  have  a  logical  division,  —  a  divi- 
sion which  makes  it  possible  to  predicate  of  each 
species  the  genus  which  has  been  divided.  If,  on 
the  other  hand,  'organism'  is  divided  into  'living 
creature/  'capable  of  locomotion/  'quadruped/  etc., 
this  is  called  a  metaphysical  division,  —  a  division 
which  makes  it  possible  to  predicate  of  the  genus 


DIVISION   AND   CLASSIFICATION  195 

each  of  the  attributes  which  the  division  distin- 
guishes. The  purpose  of  physical  division  is  to  anal- 
yse a  whole  or  aggregate  into  the  parts  of  which 
it  is  composed.  Thus,  we  may  divide  'horse'  into 
head,  legs,  ears,  tail,  etc.  This  process  is  sometimes 
called  physical  partition.  It  is  distinguished  from 
the  other  kinds  of  division  by  the  fact  that  neither 
parts  nor  wholes  can  be  predicated  of  each  other. 
For  example,  it  is  obvious  that  'horse'  is  neither 
head,  nor  legs,  nor  ears,  etc.;  nor  can  we  say  of 
any  one  of  these  that  it  is  horse.  Verbal  division  is 
sometimes  mentioned  as  a  separate  form  of  division. 
It  is  used  to  denote  the  act  of  distinguishing  the 
homonymous  meanings  of  a  word.  For  example,  the 
word  'hand'  may  mean  either  'a  labourer'  or  'an 
organ  of  the  human  body.' 

Fundamentum  Divisionis.  We  have  seen  that  the 
motive  to  logical  division  is  found  in  the  interest 
we  have  in  determining  the  whole  denotation  of  a 
term's  meaning.  Logical  division  is,  therefore,  the 
method  by  which  we  systematically  develop  the  de- 
notation of  terms  whose  meanings  have  been  fixed 
by  definition.  It  follows  from  this  that  we  cannot 
divide  a  term  whose  meaning  is  unknown  to  us. 
This  fact  is  frequently  overlooked  by  the  student, 
and  he  is  apt  to  make  the  effort  to  put  the  method 
into  operation  in  a  case  in  which  his  knowledge  of 
the  totum  divisum,  or  term  to  be  divided,  makes  his 
failure  a  foregone  conclusion.  Logical  division  pre- 
supposes that  the  totum  divisum  has  been  given  a 
meaning  by  logical  definition.  If,  consequently,  we 


196  A   TEXT-BOOK   OF   LOGIC 

are  required  to  determine  the  denotation  of  a  term 
with  whose  connotation  we  are  unacquainted,  we 
must  first  determine  the  meaning  of  that  term  by 
the  method  of  logical  definition.  While,  therefore, 
logical  division  and  logical  definition  are,  as  we 
have  seen,  closely  related  processes,  each  has  a  dis- 
tinctive role  to  play  in  the  development  of  meaning. 
With  this  caution  in  mind,  we  pass  to  a  statement 
of  certain  features  of  the  method  of  logical  division 
which  throw  light  upon  the  significance  of  the  proc- 
ess itself.  What,  we  may  ask,  is  the  basis  of  divi- 
sion? On  what  principle  or  principles  are  we  to 
proceed  in  any  given  case?  By  what  are  we  to  be 
guided  in  working  out  a  logical  division?  The 
answer  to  such  questions  as  these  is  usually  given  in 
an  exposition  of  what  logicians  call  the  fundamen- 
tum  divisionis.  By  a  fundamentum  divisionis  is 
meant  some  characteristic  of  the  totum  divisum 
which,  when  systematically  applied,  develops  differ- 
ences among  its  members.  Or,  as  it  is  sometimes 
said,  it  is  that  aspect  of  the  genus  in  respect  of 
which  its  species  are  differentiated.  If,  now,  the 
purpose  of  logical  division  is  to  develop  differences 
in  respect  of  which  species  may  be  differentiated, 
we  shall  have  to  seek  in  our  definition  of  the  totum 
divisum  for  some  indeterminate  attribute  which 
can  serve  as  the  basis  of  our  division.  Now  that 
there  should  be  something  indeterminate  in  a  defini- 
tion will  become  perfectly  clear  if  we  recollect  that 
all  that  a  definition  aims  to  give  is  a  meaning  relevant 
to  the  situation  and  purpose  which  made  the  defini- 


DIVISION  AND   CLASSIFICATION  197 

tion  necessary.    There  is  no  such  thing  as  a  complete 
definition  in  any  other  sense  than  a  relevant  defini- 
tion.    The  only  other  sense  in  which  we  can  speak 
of  definitions  being  complete  is  that  we  are  ac- 
quainted with  all  the  known  meanings  of  a  word. 
But  in  that  case  we  should  not  have  a  single  defini- 
tion but  a  series  of  definitions;  and,  of  course,  all 
that  we  could  say  about  that  is  that  the  series  is 
complete,  not  that  the  definition  is.    If,  consequently, 
our  definition  of  a  term  enables  us  to  make  unam- 
biguous statements,  that  is  all  that  we  can  expect 
of  it;  but  it  does  not  follow  that  the  definition  will 
be  sufficiently  determinate  for  carrying  out  a  logical 
division.     For  example,  'man*  has  been  defined  as 
a  rational  animal,  and,  as  a  definition,  it  serves  its 
purpose  well  enough.    But  if  we  consider  the  deno- 
tation of  the  term's  meaning  thus  defined,  we  shall 
find  that  there  is  something  indeterminate  in  the 
word  rational,  for  rationality,  as  we  all  know,  ad- 
mits of  degrees.    When,  therefore,  we  assert  of  any 
individual  that  he  is  a  man,  that  is,  a  rational  ani- 
mal, we  cannot  be  understood  to  imply  a  definite 
degree  of  rationality,  but  only  some  degree.     If, 
however,  we  asked  what  degrees  of  rationality  exist, 
we  should  have  to  adopt  some  standard  of  ration- 
ality, or  state  more  carefully  what  we  mean  by 
rationality  in  our  definition  of  man.    This  standard 
or  statement  would  be,  for  the  purpose  of  logical 
division,  our  fundamentum  divisionis.    With  respect 
to  this  fundamentum  divisionis,  some  individuals 
will  meet  the  requirements  it  lays  down,  and  these 


198  A   TEXT-BOOK   OF   LOGIC 

we  call  normal ;  others  will  fail  to  meet  it,  and  these 
we  call  abnormal.  In  the  latter  class,  we  find  some 
who  fall  below,  and  some  who  fall  above  the  stan- 
dard :  the  sub-normal  and  the  super-normal  respect- 
ively. The  sub-normal,  again,  may  be  divided  into 
dements,  those  in  whom  mental  deficiency  appears 
subsequently  to  mental  development,  and  aments, 
those  who  have  never  attained  normal  mental  devel- 
opment. The  aments  may  be  divided,  according  to 
the  degree  in  which  they  depart  from  the  normal, 
into  feeble-minded,  imbecile,  idiot.  This  division 
may  be  shown  in  tabular  form  as  follows: 

Man 

A 


N«rmal  Abnormal 

A 


Sub-normal  Super-normal 


Dements  Aments  Genius 

^_ A 

f  \ 

Feeble-minded    Imbecile    Idiots 

We  may  point  out  in  this  connection  that  every 
division  reacts  upon  the  definition  from  which  it 
starts  to  make  it  more  exact.  For  example,  we 
found  the  definition  of  man  as  a  rational  animal 
defective  because  it  neither  stated  what  is  meant 
by  rationality,  nor  what  degrees  of  rationality  were 
to  be  recognised.  .  Both  these  deficiencies  are  made 
good  in  logical  division.  Thus,  to  make  our  funda- 
mentum  divisionis  clear,  we  may  say  that  by  ration- 
ality we  mean  'a  degree  of  intellectual  capacity  suffi- 


DIVISION  AND  CLASSIFICATION  199 

cient  to  enable  its  possessor  to  perform  his  duties 
as  a  member  of  society  in  that  position  of  life  to 
which  he  is  born/  and  the  classes  of  those  who  ful- 
fill these  standard  requirements  or  depart  from 
them  either  by  way  of  excess  or  defect  are  the 
normal,  dements,  feeble-minded,  imbecile,  idiot, 
genius.  When,  therefore,  we  look  back  upon  the 
original  definition  from  the  standpoint  of  our 
completed  division,  it  has  taken  on  a  more  definite 
meaning.  We  now  know  not  only  what  is  specifically 
meant  by  calling  any  man  rational,  but  we  also  know 
what  are  the  different  degrees  in  which  rationality 
may  in  any  case  be  realised.  In  other  words,  our 
division  enables  us  to  say  that  the  concept  'man,' 
when  determined  with  respect  to  rationality,  may 
be  realised  in  either  one  or  the  other  of  the  forms 
specified  in  the  division. 

Questions  of  Terminology.  We  shall  postpone 
further  discussion  of  the  problems  of  logical  divi- 
sion until  we  have  explained  the  technical  terms  in 
which  the  discussion  must  be  carried  on.  For  the 
sake  of  completeness,  we  may  recall  that  the  term 
totum  divisum  was  used  above  to  denote  the  whole 
that  is  divided;  it  is  the  genus  with  which  any 
division  starts.  When  viewed  in  relation  to  all  the 
species  to  which  logical  division  gives  rise,  the 
totum  divisum  is  called  the  summum  genus.  The 
species  with  which  a  division  ends  are  called  in- 
firmae  species.  If,  as  in  the  illustration  used  in 
the  last  section,  our  division  is  carried  through  a 
number  of  stages,  the  intermediate  species,  that 


200  A  TEXT-BOOK   OF  LOGIC 

is,  those  that  fall  under  the  summum  genus,  are 
spoken  of  as  subaltern  genera.  When,  however, 
we  wish  to  point  out  the  relation  that  any  one  of  the 
subaltern  genera  has  to  the  next  below  it  in  the 
series,  we  designate  this  subaltern  genus  the  prox- 
imum  genus.  It  will  be  observed  that  the  totum 
dioisum  is  a  proximate  genus  with  respect  to  the 
next  below  it  in  the  series,  but  a  summum  genus 
with  respect  to  all,  —  whether  one  or  more,  —  that 
lie  below  it  in  the  series.  The  constituent  or  co- 
ordinate species  are  those  which  are  differentiated 
at  any  single  stage  in  the  process  of  logical  division. 
These  distinctions,  it  should  be  noted,  are  purely 
relative,  and  the  student  will  have  no  difficulty  in 
mastering  the  terminology  if  he  observes  that  they 
all  hinge  upon  the  meaning  assigned  to  genus  and 
species.  A  genus  is  anything  considered  as  a  sub- 
ject of  division,  and  a  species  is  always  the  end- 
product  of  a  division.  The  same  thing,  therefore, 
may  be  both  a  genus  and  a  species,  but  whenever 
that  is  the  case,  the  same  thing  is  being  looked  at 
from  different  points  of  view. 

Rules  of  Logical  Division.  There  are  other  fea- 
tures of  logical  division  than  those  that  have  been 
already  considered  with  which  it  is  important  that 
the  student  should  become  acquainted.  These  we 
shall  state  and  illustrate  in  connection  with  our 
enumeration  and  exposition  of  the  rules  of  logical 
division. 

The  first  rule  is  that  a  logical  division  must  pro- 
ceed in  all  its  stages  upon  one  fundamentum  divi- 


DIVISION  AND  CLASSIFICATION  201 

sionis.  The  reason  for  this,  of  course,  is  found  in 
the  nature  of  the  problem  that  logical  division  is 
set  to  solve.  That  problem  is  to  develop  the  mean- 
ing of  a  term  so  as  to  make  determinate  whatever 
may  have  been  left  indeterminate  in  its  definition. 
If  we  did  not  keep  within  that  aspect  of  a  term's 
meaning  with  which  our  logical  division  starts, 
we  should  fail  to  develop  this  meaning  from  an  in- 
determinate to  a  more  determinate  form.  In  the 
example  used  above,  we  found  that  a  number  of  de- 
grees of  rationality  exist,  and  that  these  must  be 
included  in  our  definition  of  'man'  if  this  concept  is 
to  be  completely  determined.  If  we  had  found,  in 
our  division  of  the  term,  species  of  another  kind,  — 
let  us  say  red  man,  yellow  man,  —  it  would  be  evi- 
dent that  we  had  gone  outside  the  fundamentum 
divisionis,  rationality,  and  that  we  had  consequently 
failed  to  determine  that  aspect  of  the  term's  meaning 
with  which  we  were  concerned.  Whenever  this  hap- 
pens, whenever,  that  is,  we  fail  to  carry  the  division 
through  on  a  single  principle,  we  are  said  to  have  a 
cross  division.  All  the  species  to  which  a  logical 
division  gives  rise  must  be  the  same  in  kind;  and 
this  is  possible  only  if  we  retain  the  same  principle 
of  division  throughout.  Again,  in  carrying  out  a 
principle  of  division,  we  aim  to  make  our  species 
exclusive,  to  include,  that  is  to  say,  in  any  one  species 
only  that  which  is  definitely  excluded  by  the  other 
co-ordinate  species.  The  constituent  species  of  a 
genus  must  not  overlap.  This  requirement  is  ob- 
viously related  to  that  feature  of  a  logical  definition 


202  A  TEXT-BOOK   OF  LOGIC 

which  emphasises  the  difference  between  two  or 
more  conflicting  meanings  (differentia),  as  the 
former  requirement  connects  logical  division  with 
the  other  aspect  of  definition  which  emphasises  the 
common  likeness  of  these  conflicting  meanings 
(g enus). 

It  is  not  difficult  to  apply  the  first  rule  of  divi- 
sion when  the  fundamentum  divisionis  is  completed 
in  a  single  step.  For  example,  if  'man'  is  defined  as 
'a  rational  animal  possessing  a  skin-color  of  some 
kind/  the  latter  part  of  the  definition  may  become 
for  us  a  principle  of  division.  Dividing  man  then 
according  to  skin-colour  we  find  the  denotation  of 
the  term  to  be  as  follows : 

Man 

^ A ^ 

f  >\ 

White  man    Black  man    Yellow  man    Brown  man    Red  man 

When,  however,  the  division  is  carried  through 
several  stages,  as  it  frequently  is,  it  may  not  be 
apparent  how  a  single  principle  can  control  the 
whole  series  of  divisions.  If,  for  example,  we  were 
to  divide  'human  being'  into  'male'  and  'female,'  and 
were  then  to  divide  'female'  into  'brunette'  and 
'blonde,'  it  is  obvious  that  the  fundamentum  divi- 
sionis in  the  first  division  is  sex  difference,  and  in 
the  second,  complexion  colour.  In  cases  like  this, 
we  cannot  look  upon  the  division  as  a  series  which 
develops  a  single  theme;  we  must  regard  it  rather 
as  a  chain  of  discontinuous  divisions  which  contains 
as  many  separate  divisions  as  there  are  distinct 
fundamenta.  The  fact  that  they  can  be  written 


DIVISION  AND  CLASSIFICATION  203 

consecutively  does  not  have  any  logical  significance ; 
the  reason  for  giving  this  form  to  them  is  econom- 
ical; it  saves  time,  when  the  end  product  of  one 
division  is  the  starting-point  of  a  new  one,  to  con- 
tinue in  the  serial  order.  If,  however,  our  practice 
were  guided  by  logical  requirements,  we  should  re- 
write our  term  whenever  we  intend  to  apply  to  it  a 
new  principle  of  division. 

Let  us  now  consider  the  case  of  a  division  which 
has  the  characteristics  of  a  continuous  series,  that 
is,  a  series  which  develops  a  single  idea  through  a 
number  of  stages.  The  significance  of  this  case  is 
that  it  emphasises  the  importance  and  illustrates 
the  method  of  systematically  developed  knowledge, 
of  knowledge,  that  is,  which  proceeds  at  each  step  by 
the  smallest  possible  degrees  of  relevant  difference. 
Thus,  in  carrying  out  a  division  which  develops  its 
meaning  in  a  continuous  series,  we  are  counselled  to 
make  the  steps  of  the  series  as  small  as  possible.  This 
is  the  purport  of  the  Latin  injunction,  Divisio  ne  fiat 
per  saltum:  you  must  not  make  your  division  go 
by  leaps.  A  division  that  is  not  systematically  de- 
veloped is  useless  for  the  purpose  that  put  it  in  oper- 
ation. But  since,  throughout  all  the  stages  that  we 
carry  our  division,  we  need  to  be  guided  by  a  single 
principle,  it  is  evident  that  at  each  stage  of  the  divi- 
sion we  must  use  a  fundamentum  divisionis  that  is 
some  modification  of  the  principle  with  which  we 
began  the  division.  That  is  to  say,  each  subordinate 
fundamentum  must  fall  within  the  meaning  of  the 
original  fundamentum.  An  illustration,  borrowed 


204  A   TEXT-BOOK   OF  LOGIC 

from  Gibson,  will  make  this  evident.  Let  us  take 
as  our  fundamentum  divisionis,  the  side-relations  of 
'quadrilateral  figures,'  understanding  by  quadrilat- 
eral figure  'a  plane  rectilinear  quadrilateral  figure.' 
Our  purpose  is  to  develop  the  number  of  types  which 
belong  to  this  class.  According  to  their  side-rela- 
tions, 'quadrilateral  figures'  are  either  'parallelo- 
grams/ that  is,  figures  whose  opposite  sides  are 
parallel  and  equal,  or  'non-parallelograms.'  Divid- 
ing these  species  further  according  to  the  inclination 
of  their  sides,  a  special  form  of  the  original  funda- 
mentum,  we  get,  in  the  case  of  the  parallelograms, 
rectangle  and  non-rectangle ;  and  in  the  case  of  the 
non-parallelograms  trapezium,  a  figure  in  which 
there  are  no  parallel  sides,  and  trapezoid,  a  figure  in 
which  two  of  the  sides  are  parallel  but  not  equal. 
Another  specification  of  the  original  fundamentum 
would  be  relative  side-length.  If  we  apply  this  to 
rectangle  we  get  square  and  oblong;  and  to  non- 
rectangle,  rhombus  and  rhomboid,  oblique  figures 
which  correspond  to  the  square  and  oblong  respect- 
ively. All  these  relations  expressed  in  the  form  of 
a  genealogical  tree  are  as  follows: 

Quadrilateral  Figure 


Parallelogram  Non-parallelogram 


Rectangle  Non-rectangle       Trapezium     Trapezoid 


Square     Oblong     Rhombus     Rhomboid 


DIVISION   AND   CLASSIFICATION  205 

The  second  rule  is  that  a  logical  division  must 
be  exhaustive.  The  reason  for  this  rule  is  connected 
obviously  with  the  purpose  that  controls  such  divi- 
sion, namely,  to  denote  in  orderly  relation  whatever 
belongs  to  a  certain  genus.  What  the  rule  states 
is  that  a  place  must  be  found,  when  the  division  has 
been  made,  for  everything  that  belongs  to  the  genus 
in  one  or  other  of  the  constituent  species.  It  is  only 
another  way  of  stating  the  purport  of  the  rule  to 
say  that  the  constituent  species  together  must  be 
coextensive  with  the  whole  genus.  The  rule  is  in- 
tended to  guard  against  too  narrow  and  too  broad 
division.  When  the  division  is  too  narrow  some- 
thing is  omitted  from,  and  when  the  division  is  too 
broad  something  is  added  to,  the  genus,  and  which- 
ever fault  we  may  fall  into,  the  division  is  rendered 
useless.  Instances  of  too  narrow  division  are :  'men' 
into  'good'  and  'bad;'  and  'objects'  into  'useful'  and 
'ornamental.'  Too  broad  division  is  likely  to  occur 
whenever  there  is  an  indistinct  apprehension  of  the 
connotation  of  the  terms  we  employ  in  our  divisions. 
Unless,  therefore,  a  division  is  exhaustive,  that  is, 
neither  too  narrow  nor  too  broad,  we  have  not  really 
divided  at  all ;  for  when  the  division  is  too  narrow, 
the  constituent  species  are  equivalent  to  only  part  of 
the  genus,  and  when  it  is  too  broad,  they  are  equiv- 
alent to  the  genus  and  something  else.  Whenever  a 
genus  has  been  properly  divided,  the  denotation  of 
genus  and  species  must  exactly  coincide. 

Dichotomy.  Our  discussion  of  logical  division 
has  emphasised  two  things:  (1)  that  our  ability  to 


206  A   TEXT-BOOK   OF   LOGIC 

use  the  method  depends  upon  our  knowledge  of  the 
subject  to  which  it  is  applied,  and  (2)  that  to  insure 
against  omitting  anything  that  really  belongs  to  a 
genus  we  must  make  our  division  exhaustive,  and 
that  when  this  requires  us  to  carry  the  division 
through  several  stages,  the  steps  between  one  sub- 
division and  another  must  be  made  as  small  as  pos- 
sible. Division  is  not,  consequently,  an  easy  method 
to  apply,  although  it  is  not  difficult  to  understand; 
but  the  difficulty  is  due  primarily  to  the  great  com- 
plexity of  the  material  that  nature  presents  for  our 
study. 

Dichotomy  is  a  traditional  method  of  division 
which  has  been  supposed  to  relieve  us  of  the  diffi- 
culties to  which  we  have  just  referred,  and  to  make 
it  possible,  in  the  absence  of  any  considerable  knowl- 
edge of  the  subject  under  investigation,  to  deter- 
mine the  species  which  may  belong  to  it.  If  this 
were  true,  we  might  omit  the  consideration  of  it 
entirely  on  the  ground  that  it  is  a  merely  formal 
process ;  if  it  is  not  true,  we  must  consider  its  value 
in  relation  to  our  effort  to  make  our  knowledge  of 
things  systematic.  That  it  is  not  true  is  the  position 
of  modern  logicians  as  it  was  of  Aristotle.  We  must, 
therefore,  place  this  method  in  its  relation  to  our 
foregoing  discussions. 

First,  let  us  inquire  how  dichotomy  differs  from 
the  form  of  division  which  we  have  just  considered. 
The  characteristic  of  a  dichotomous  division  is,  as 
the  name  implies,  that  it  proceeds  at  each  step  of 
the  division  by  dividing  a  genus  into  two  alternative 


DIVISION  AND  CLASSIFICATION  207 

species.  Now,  if  each  step  of  such  a  division  ex- 
hausts the  genus  we  are  dividing,  it  is  apparent  that 
one  of  the  terms  must  be  an  indefinite  or  so-called 
negative  term.  Thus,  if  we  divide  'triangle'  accord- 
ing to  the  relations  of  the  sides,  we  shall  have  at 
the  first  division,  if  we  take  equality  of  all  the  sides 
as  the  fundamentum,  two  species,  'equilateral'  and 
'non-equilateral.'  Dividing  the  'non-equilateral' 
term  with  reference  to  the  equality  of  two  of  the 
sides,  we  shall  have  once  more  two  species,  'isosceles' 
and  'non-isosceles.'  If  we  divide  now  the  'non- 
isosceles'  term  on  the  basis  of  the  only  remaining 
possibility,  namely,  the  equality  of  one  side  with 
itself,  we  get  also  two  species,  'scalene'  and,  if  there 
are  any,  'non-scalene.'  The  arrangement  of  these 
divisions  in  a  tree  will  illustrate  the  typical  form 
of  division  by  dichotomy.  Thus: 

Triangle 

A 


Equilateral  Non-equilateral 


Isosceles  Non-isosceles 


"N 

Scalene  Non-scalene 

From  the  foregoing  statements  and  illustration, 
it  will  be  apparent  that  we  cannot  begin  to  divide 
a  term  by  dichotomy  without  having  before  our 
minds  some  definition  of  the  genus  that  we  wish  to 
divide.  Unless  we  knew,  for  example,  that  a  tri- 
angle was  'a  plane  figure  bounded  by  three  straight 
lines,'  we  should  not  be  able  to  divide  it  to  determine 


208  A  TEXT-BOOK   OF  LOGIC 

its  species.  Dichotomy,  as  much  as  any  form  of  divi- 
sion, presupposes  definition.  Now,  the  connection 
between  dichotomy  and  definition  per  genus  et  differ- 
entiam,  may  be  expressed  by  saying  that  every  such 
division  suggests  a  definition  of  the  class  we  are 
dividing,  and  that  every  definition  implies  a  division 
by  dichotomy.  Thus,  to  take  the  illustration  already 
used,  a  'triangle'  may  be  defined  as  'a  three-sided 
plane  figure  whose  sides  have  a  certain  relation  to 
each  other;'  and  if  we  wish  to  make  the  indeter- 
minate part  of  this  definition  determinate,  we  divide 
by  dichotomy  in  order  to  bring  out  the  specific  rela- 
tionship of  the  sides  to  each  other. 

We  may  observe,  further,  that,  applied  to  rela- 
tively simple  cases,  dichotomy  is  a  rather  cumber- 
some method  of  doing  what  can  be  accomplished 
more  expeditiously  at  a  single  step.  There  is  no 
reason,  for  example,  why  we  should  not  divide  tri- 
angle into  its  constituent  species  at  once ;  for,  in  such 
a  case,  it  is  not  by  the  method  of  division,  but  by 
reason  of  our  acquaintance  with  the  subject-matter, 
that  we  know  the  species  that  our  division  is  a  means 
of  classifying.  We  may  also  observe  that  it  is  un- 
avoidable in  division  by  dichotomy  that  the  end- 
product  should  be  a  hypothetical  term,  —  'non- 
scalene'  in  the  case  above  —  on  the  existence  or  non- 
existence  of  which  the  division  itself  can  throw  abso- 
lutely no  light. 

What  now,  it  may  be  asked,  is  the  value  of  a 
division  by  dichotomy?  It  is  valuable  in  the  first 
place  as  a  test  of  the  accuracy  and  exhaustiveness 


DIVISION   AND   CLASSIFICATION  209 

of  our  analysis  of  a  term's  meaning.  To  take  an 
illustration  from  Aristotle,  we  may  classify  the 
Predicables  as  follows: 

Predicables 


Commensurable  Non-commensurable 


f  \  r 


Essence  Not  essence  Part  of  essence  Not  part  of  essence 
(Definition)  (Proprium)  (Genus  or  Differentia)  (Accidens) 

It  will  be  noticed  in  this  case  that  the  fundamentum 
divisionis,  or,  as  we  may  say,  the  differentia,  is  the 
relation  of  the  species  according  to  the  degrees  of 
the  essential  connection  that  they  severally  have  to 
the  genus,  and  that  the  division  is  throughout  dich- 
otomous.  But,  of  course,  the  Predicables  were  al- 
ready known  before  they  could  serve  as  an  illustra- 
tion of  how  dichotomy  may  verify  a  classification. 

We  may  also  point  out  that  a  division  by  dich- 
otomy is  also  valuable  if  we  wish  to  ascertain  the 
position  of  a  particular  species  in  the  class  to  which 
it  belongs.  Thus,  to  quote  Welton,  "in  the  Analytic 
Key  prefixed  to  Bentham's  British  Flora,  which  is 
intended  to  enable  anyone  who  has  a  specimen  of  a 
certain  plant  before  him  to  discover  its  species  and 
its  technical  name,  the  arrangement  is  nearly  en- 
tirely dichotomous,  and,  for  such  a  purpose,  this 
form  is  the  most  useful.  But  to  adopt  dichotomy  as 
a  final  arrangement  would  be  absurd.  A  botanist,  for 
example,  starts  at  once  with  three  classes  of  the  sum- 
mum  genus  plant,  viz.,  exogens,  endogens,  and  acro- 

H 


210  A  TEXT-BOOK   OF  LOGIC 

gens,  and  each  of  these  is  sub-divided  into  varying 
numbers  of  orders,  and  these  again  into  still  further 
varying  number  of  genera,  and  so  on,  with  little  or 
no  regard  to  dichotomy,  the  object  being  to  make  the 
classification  agree  with  the  distinctions  existing 
in  the  plants  themselves." 

The  Tree  of  Porphyry.  In  a  typical  division  by 
dichotomy,  as  we  saw  in  the  last  section,  it  is  the 
negative  or  indeterminate  term  that  lends  itself  to 
further  division.  If,  now,  the  division  proceeds 
through  all  its  stages  by  the  dichotomous  division 
of  the  r^oaitiy^L  or  determinate  term,  we  have  a  spe- 
cies of  division  which  is  illustrated  by  what  is  tech- 
nically known  as  the  'Tree  of  Porphyry/  An  illus- 
tration will  show  not  only  the  possibility  of  such  a 
division,  but  exhibit  the  form  that  is  characteristic 
of  it.  Thus: 

Substance 


Corporeal  Incorporeal 


f  \ 

Animate  Inanimate 


Sensible  Insensible 


Rational         Irrational 

In  any  case  of  division  by  dichotomy  whether  of 
this  type  or  not,  the  indeterminate  or  negative  term 
and  the  determinate  or  positive  term,  in  their  rela- 
tion to  each  other,  are  sometimes  referred  to  as 
Contradictory  Opposites,  Contradictory  Relatives, 
or  Contradictories.  This  designation  is  apt  to  be 


DIVISION   AND  CLASSIFICATION  211 

misleading  unless  it  is  pointed  out  that  contradic- 
tion can  be  logically  postulated  of  terms  only  when 
these  have  a  common  or  underlying  basis.  There  is 
no  contradiction,  for  example,  between  virtue  and 
beef-steak,  because  they  do  not  belong  to  the  same 
universe  of  discourse,  that  is,  because  they  have  no 
common  basis.  Animate  and  inanimate  are  contra- 
dictories because  they  are  the  alternative  ways  in 
which  corporeal  substance  is  capable  of  getting  itself 
expressed.  The  alternative  species,  therefore,  to 
which  a  dichotomous  division  gives  rise  may  be 
spoken  of  as  contradictory  in  the  sense  that  they 
are  the  definite  and  exclusive  forms  in  which  the 
genus  to  which  they  belong  is  realised.  It  would, 
perhaps,  avoid  all  ambiguity  if  we  spoke  of  the  rela- 
tion between  the  determinate  and  indeterminate 
terms  of  a  logical  division  as  Complementary*  If 
we  did  so,  we  should  have  to  mean  that  the  indeter- 
minate term  included  within  it  all  of  the  denotation 
of  the  genus  that  was  not  definitely  included  in  the 
determinate  term.  Only  on  this  interpretation  can 
these  terms  be  regarded  as  the  names  of  alternate 
species. 

It  will  be  observed  that  in  a  division  of  the  type 
illustrated  by  the  Tree  of  Porphyry  the  indetermin- 
ate term  is  rejected  at  each  of  the  subordinate  steps. 
This  fact  is  technically  known  as  an  abscissio  in- 
finiti. 

Classification  Defined.  One  does  not  need  to  go 
to  text-books  of  logic  to  become  acquainted  with  the 
process  that  is  denoted  by  the  term  classification. 


212  A   TEXT-BOOK   OF  LOGIC 

Before  he  has  entered  the  university,  nay  before  he 
has  entered  the  common  school,  the  normal  child 
has  learned  to  arrange  the  objects  with  which  he  is 
brought  daily  into  contact  into  groups,  and  to  do 
this  on  the  basis  of  their  observed  likenesses  and 
unlikenesses.  Whenever  anyone  groups  objects  to- 
gether on  the  ground  of  their  likenesses,  and  dis- 
tinguishes between  groups  on  the  ground  of  their 
differences,  he  is  employing  the  method  of  classifi- 
cation. Classification,  therefore,  may  be  defined  as 
the  process  of  thinking  together  a  number  of  objects 
on  the  ground  of  their  common  attributes,  and  of 
thinking  apart  groups  of  objects  whose  attributes 
are  different. 

Classification  and  Definition.  It  will  be  seen  that 
classification,  as  thus  defined,  is  closely  related  to 
definition.  Definition  completes  the  process  that  is 
begun  in  classification.  Classification  underlies  the 
defining  process.  This  relationship  will  become  evi- 
dent if  we  recall  that  definition  aims  to  place  the 
object  whose  meaning  is  not  clear  in  a  class  with 
other  objects  which  share  with  it  a  common  set  of 
attributes.  When,  therefore,  we  ask  how  we  can 
find  the  genus  of  any  term  we  wish  to  define,  the 
answer  will  point  us  to  the  method  of  classification 
which  we  are  now  studying.  This  is  only  another 
way  of  saying,  with  a  slightly  different  emphasis, 
what  was  said  in  the  last  chapter,  namely,  that  the 
method  of  definition  is  based  upon  the  comparison 
of  the  object  we  are  defining  with  other  objects  that 
are  in  danger  of  being  confused  with  it.  Compar- 


DIVISION  AND   CLASSIFICATION  213 

ison  is  common  both  to  definition  and  to  classifica- 
tion. But  we  compare  objects  with  each  other  in  clas- 
sification for  the  purpose  of  ascertaining  their  com- 
mon attributes;  in  definition,  we  compare  the  ob- 
jects of  a  class  for  the  purpose  of  discovering  the 
differences  which  keep  the  sub-classes  distinct.  This 
statement  has  important  practical  and  philosophical 
bearings.  It  enables  us  to  see,  for  instance,  how 
groups  of  objects  can  be  considered  as  a  single  ob- 
ject, a  fact  that  gives  significance,  as  we  have  seen, 
to  the  general  concrete  term.  Whenever  we  over- 
look the  differences  between  the  objects  of  which 
a  class  is  composed,  and  emphasise  the  points  of 
likeness  by  which  each  object  retains  its  place  in 
the  class,  we  have  constituted  of  the  class  a  distinct 
kind  of  object.  In  such  a  class  the  individuals  are 
no  longer  important,  there  is  no  discernible  differ- 
ence between  one  and  another ;  they  are,  as  Leibnitz 
would  say,  identical.  But  if,  for  any  reason,  the 
statements  we  make  were  dependent  for  their  clear- 
ness upon  the  differences  in  the  class,  we  should 
have  to  go  beyond  the  method  of  classification  by 
which  our  classes  are  constituted,  and  we  should  be 
forced,  as  we  have  pointed  out,  to  adopt  the  method 
of  definition.  In  classification,  we  are  interested  in 
the  likenesses,  in  definition,  in  the  differences  of 
objects. 

Classification  and  Division.  Whenever  we  are  in 
danger  of  overlooking  the  distinctions  that  exist 
within  a  genus,  whenever,  that  is,  we  are  in  danger 
of  making  ambiguous  statements  through  our  fail- 


214  A   TEXT-BOOK   OF   LOGIC 

ure  to  keep  in  mind  the  whole  denotation  of  a  term, 
there  exists  a  situation  that  may  be  relieved  by  the 
employment  of  the  method  of  division.  The  starting 
point  of  a  logical  division  is  the  genus,  the  whole 
which  is  possessed  of  a  number  of  common  qualities ; 
and  the  purpose  of  division  is  to  mark  out  within 
the  genus  the  species  which  realise,  in  different 
ways,  these  common  qualities.  The  movement  of 
thought  is  downward  from  the  more  general  to  the 
less  general.  If  now  we  consider  the  characteristics 
of  a  classification,  we  shall  find  that  they  are  the 
reverse  of  this.  The  situation  in  which  we  feel 
obliged  to  classify  is  one  in  which  we  are  in  danger 
of  failing  to  observe  the  likenesses  of  objects  on 
account  of  the  prominence  that  their  individual 
attributes  have  come  to  assume.  Popularly  ex- 
pressed, we  are  exposed  to  the  danger  of  "missing 
the  wood  for  the  trees."  The  starting  point  of  all 
classification,  therefore,  is  the  particular,  the  objects 
which  are  kept  distinct  and  apart  on  account  of 
their  differences ;  and  the  purpose  that  classification 
is  intended  to  serve  is  to  detect  within  these  differ- 
ences certain  relatively  permanent  groups  of  qual- 
ities. Our  most  available  method  for  doing  this  is 
comparison;  but  that  in  respect  of  which  the  com- 
parison is  made  is  determined  by  the  interest  that 
our  classification  is  to  promote.  For  instance,  we 
may  classify  objects  with  respect  to  their  use  or 
with  respect  to  their  sense-attributes.  It  is  the 
character  of  our  interest  in  things  that  determines 
which  of  these  principles  of  classification  we  choose ; 


DIVISION   AND   CLASSIFICATION  215 

but,  in  any  case,  the  movement  of  thought  in  class- 
ification is  upward  from  the  particular  to  the  gen- 
eral. Classification  is  the  beginning  of  a  process 
that  we  shall  study  more  in  detail  when  we  come  to 
the  problem  of  induction. 

Kinds  of  Classification.  It  has  been  customary 
to  distinguish  two  kinds  of  classification,  —  the  arti- 
ficial and  the  natural.  By  an  artificial  classification 
is  usually  meant  one  in  which  the  grouping  of  ob- 
jects takes  place  on  the  ground  of  their  possessing 
some  attribute  or  group  of  attributes  which  does  not 
serve  as  the  basis  of  any  further  statement  about 
these  objects.  We  may,  for  example,  classify  cer- 
tain objects  of  domestic  furniture  as  chairs;  but 
having  done  so,  we  are  not  able,  on  that  basis,  to 
predicate  anything  further  of  the  objects  to  which 
the  name  chair  is  given.  By  a  natural  classification 
is  generally  meant  one  that  groups  objects  on  the 
ground  of  their  possessing  an  attribute,  or  group  of 
attributes,  which  serves  as  the  basis  of  further  pred- 
ication. For  example,  if  we  classify  a  group  of  ani- 
mals as  mammals,  we  are  able  to  say,  by  virtue  of 
the  fact  that  they  are  mammals,  that  they  are  also 
vertebrates.  This  view  has  received,  among  modern 
writers,  a  classic  expression  by  Mill.  It  is  based 
upon  the  supposition  that  there  exist  in  nature 
classes  of  objects  which  are  distinct  from  each  other, 
and  that  if  we  make  the  differences  of  these  classes 
the  basis  of  our  classification,  we  shall  thereby  mark 
off  the  'natural  kinds'  from  others  which  by  way  of 
contrast  may  be  called  artificial  kinds. 


216  A   TEXT-BOOK   OF  LOGIC 

Since  the  spread  of  the  doctrine  of  evolution,  it 
is  no  longer  possible  to  maintain,  in  all  fields  of 
knowledge,  the  distinction  of  natural  and  artificial 
kinds.  We  no  longer  think  of  species  of  animals, 
for  example,  as  marking  fixed  and  distinct  differ- 
ences between  groups  of  objects;  we  have  to  think, 
according  to  the  doctrine  of  evolution,  of  the  whole 
animal  series,  from  amoeba  to  man,  as  having 
sprung  from  a  common  ancestor.  Species  are  not, 
in  the  meaning  of  the  distinction  we  are  now  con- 
sidering, separate  and  distinct  kinds. 

But  while  we  no  longer  find  it  possible  to  classify 
objects  in  the  way  just  considered,  the  distinction 
between  natural  and  artificial  suggests  a  truth  of 
which  we  may  take  advantage  in  our  discussion  of 
this  topic.  The  fallacy  that  underlies  the  separation 
of  classes  into  natural  and  artificial  seems  to  be, 
from  the  logictl  standpoint,  that  it  denies  that  rele- 
vancy to  purpose  is  a  factor  in  all  classification.  The 
classification  of  objects,  for  example,  as  natural  is 
based  on  the  supposition  that  the  attributes  of  spe- 
cies are  determined  wholly  by  the  nature  of  the  ob- 
jects themselves,  and  that  they  are  in  no  way  and  to 
no  extent  determined  by  the  interest  which  prompts 
us  to  classify;  while  the  classification  of  objects  as 
artificial  is  predominantly,  if  not  wholly,  determined 
by  the  interest  that  controls  the  classification.  This 
can  not  be  maintained.  For,  as  we  have  seen,  knowl- 
edge is  always  the  product  of  both  kinds  of  factors,— 
of  both  subjective  purpose  and  objective  fact.  And 
it  is  this  analysis  of  what  we  mean  by  knowledge 


DIVISION   AND   CLASSIFICATION  217 

that  gives  us  the  clue  to  the  distinction  of  natural 
and  artificial  kinds,  and  which  enables  us  to  under- 
stand the  two  main  kinds  of  classification.  Our 
classification  does  not  depend  upon  the  presence  or 
absence  of  interest,  but  upon  the  particular  kind  of 
interest  which  we  seek  to  satisfy.  We  may  be  in- 
terested, for  example,  in  grouping  objects  according 
to  their  essential  attributes,  that  is,  according  to 
the  attributes  which  constitute  them  members  of  a 
class.  We  may  also  be  interested  in  grouping  ob- 
jects according  to  their  non-essential  attributes, 
that  is,  according  to  the  attributes  which  are  either 
implied  by  their  essential  attributes,  or  which  are 
only  accidental  ones.  In  view  of  our  discussion  of 
the  Predicables,  this  statement  means  that  we  may 
make  the  qualities  which  characterise  the  genus  the 
principle  of  classification;  or  the  qualities  which 
characterise  the  proprium,  or  the  accidens,  the  basis 
of  classification. 

Classification  according  to  the  essential  attri- 
butes of  the  objects  compared  gives  a  theoretical 
classification;  and  classification  according  to  the 
non-essential  attributes,  a  practical  classification. 
In  the  former  case,  the  theoretical  interests  which 
prompt  us  to  study  the  nature  of  things  are  upper- 
most ;  and  in  the  latter,  the  practical  interests  wkich 
are  concerned  with  the  uses  of  things  are  in  control. 
To  take  an  illustration  usually  found  in  text-books 
of  logic,  the  Swedish  botanist,  Karl  Linnaeus  (1707- 
1778),  based  his  classification  of  plants  upon  the 
comparison  of  the  sexual  organs  of  plants.  The 


218  A  TEXT-BOOK   OF  LOGIC 

distinct  advantage  of  this  method  was  that  it  made 
possible  the  indexing  of  plants  in  a  convenient  way 
into  genera  and  species  so  that  their  relative  posi- 
tion to  each  other  in  a  series  could  be  made  out. 
This  must  be  taken  not  as  a  theoretical,  but  as  a 
practical  classification,  and,  in  principle,  is  not  differ- 
ent from  the  arrangement  of  words  in  a  dictionary 
in  their  alphabetical  order.  If,  on  the  other  hand, 
we  make  a  classification  according  to  the  natural 
relationships  of  the  species,  we  shall  have  an  illus- 
tration of  a  theoretical  classification.  It  will  be 
obvious  that  many  variations  are  possible  within 
these  two  divisions ;  but  for  the  details,  the  student 
is  referred  to  the  larger  books  on  logic  and  the 
principles  of  science. 

REFERENCES 

H.  A.  Aikins,  The  Principles  of  Logic,  Ch.  IV. 

J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Ch.  VI. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  V. 

W.  Minto,  Logic,  Inductive  and  Deductive,  Ch.  IV. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Ch. 
XXI. 

W.  J.  Taylor,  Elementary  Logic,  Pt.  II.,  Ch.  V. 

ADVANCED 

R.  W.  B.  Gibson,  The  Problem  of  Logic,  Chs.  IV.,  V. 

H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Chs.  III.,  V. 

F.  C.  S.  Schiller,  Formal  Logic,  Chs.  IV.,  VI.,  §§  6-10. 

C.  Sigwart,  Logic,  Pt.  II.,  §§  42-43. 

J.  Venn,  Empirical  Logic,  Chs.  XII.,  XIII. 

J.  Welton,  A  Manual  of  Logic,  Vol.  I.,  Bk.  I.,  Ch.  VI. 


DIVISION   AND   CLASSIFICATION  219 


QUESTIONS 

1.  In  what  way  is  logical  division  related  to  logical  defini- 
tion? 

2.  Name  one  way  in  which  logical  division  may  not  be  in- 
terpreted. 

3.  Explain:     By  division  we  analyse  the  denotation  of  a 
term's  meaning. 

4.  What  is  meant  by  saying  that  the  species  enumerated 
in  a  logical  division  are  to  be  read  disjunctively? 

5.  What  is  the  test  of  a  logical  division? 

6.  What  is  a  metaphysical  division,  and  how  does  it  differ 
from  a  logical  division? 

7.  What  do  you  understand  by  a  physical  division?     Illus- 
trate. 

8.  What  is  a  verbal  division? 

9.  Define  a  fundamentum  divisionis. 

10.  Explain  how  one  discovers  for  a  particular  division  an 
appropriate  fundamentum  divisionis. 

11.  In  what  respects  can  a  logical  definition  be  improved 
from  the  standpoint  of  logical  division? 

12.  Explain  the  following  terms:  genus,  species,  totum  di- 
visum,     summum     genus,     infirmae     species,     subaltern 
genera,  proximate  genus,  constituent  species. 

13.  What  is  the  first  rule  of  logical  division? 

14.  What  is  a  cross  division?     Explain  how  it  occurs. 

15.  What  is  meant  by  saying  that  the  species  to  which  a 
logical  division  gives  rise  must  be  exclusive? 

16.  What  are  the  character  and  importance  of  a  continuous 
series? 

17.  How  can  we  keep  within  a  single  fundamentum  when 
our  division  is  carried  through  a  number  of  stages? 

18.  State  and  explain  the  second  rule  of  logical  division. 

19.  What  difficulties  in  the  method  of  logical  division  are 
supposed  to  be  met  by  dichotomy? 

20.  What  are  the  characteristics  of  a  dichotomous  division? 

21.  What  is  the  relation  of  dichotomy  to  definition? 


220  A  TEXT-BOOK  OF  LOGIC 

22.  What   advantages   are   sometimes   claimed   for   a   dich- 
otomous  division? 

23.  What  is  the  Tree  of  Porphyry? 

24.  What  do  you  understand  by  contradictory  opposites? 

25.  Explain  absdssio  infiniti. 

26.  What  is  classification? 

27.  How  are  classification  and  definition  related? 

26.     What  is  the  relation  of  classification  and  division? 

29.  State  Mill's  doctrine  of  classification. 

30.  Why  has  the  distinction  of  natural  and  artificial  kinds 
broken  down? 

31.  What  is  the  relation  of  purpose  to  classification,  and 
what  effect  does  this  have  upon  the  distinction  of  nat- 
ural and  artificial  classification? 

32.  What  bases  of  classification  may  be  recognized  as  im- 
plicit in  Mill's  doctrine  of  classification? 

33.  Explain  theoretical  and  practical  classification. 

EXERCISES 

1.  Divide  logically  the  following  terms,  stating  in  each  in- 
stance (a)  the  definition  and   (b)  the  fundamentum  di- 
visionis. 

psychology  gun  culture 

European  student  government 

2.  Examine  the  following  divisions,  and  point  out  which 
rule  of  logical  division,  if  any,  is  broken  by  them: 

(1)  Substances  into  material  and  spiritual. 

(2)  Books  into  scientific,  philosophical,  and  literary. 

(3)  Religions  into  true  and  false. 

(4)  Students  into  those  who  are  diligent,  female,  and 

athletic. 

3.  What    is    the    metaphysical    division    of   the    following 
terms? 

landscape  philosophy  toy 

capital  child  amusement 


DIVISION  AND   CLASSIFICATION  221 

4.  Divide  physically  six  terms  of  your  own  selection. 

5.  Give  six  illustrations  of  verbal  division. 

6.  Illustrate  a  cross  division,  and  explain  how  it  is  brought 
about. 

7.  Give  two  examples  of  dichotomy. 

8.  Illustrate  by  two  examples  the  Tree  of  Porphyry. 

9.  Give   examples   which   illustrate   the   characteristics   of 
(a)   a  theoretical  and   (b)  a  practical  classification. 


CHAPTER  VIII 

CATEGORICAL    PROPOSITIONS 

Types  of  Propositions.  In  a  former  chapter  we 
saw  that  predication  is  the  act  of  affirming  or  deny- 
ing something  (P)  of  something  else  (S).  Any 
statement  which  rests  upon  predication,  that  is, 
which  affirms  or  denies  something  of  something  else, 
is  called  in  logic  a  proposition.  Predication  may  be 
of  various  degrees  of  directness  or  explicitness,  ac- 
cording to  the  degree  of  our  knowledge  of  the  sub- 
ject of  predication.  For  example,  if  my  knowledge 
of  natural  history  is  only  slight,  I  shall  probably  be 
able  to  say  of  a  given  animal  merely  that  it  is  either 
a  lion  or  a  tiger  or  a  leopard  or  something  else.  If 
a  further  study  of  animals  makes  me  acquainted 
with  the  characteristics  of  the  species  lion,  I  shall 
then  be  able  to  say  that  if  a  given  animal  has  these 
characteristics,  it  is  a  lion.  If,  again,  the  examina- 
tion of  a  particular  animal  showed  that  it  does  or 
does  not  have  these  distinguishing  qualities,  I  should 
then  be  able  to  say  that  it  is  or  is  not  a  lion.  The 
forms  of  predication  illustrated  in  these  instances 
we  have  learned  already  to  call  alternative,  hypo- 
thetical, and  categorically  respectively.  The  state- 
ments in  which  these  forms  of  predication  are  ex- 
pressed are  called  disjunctive,  hypothetical  and  cate- 
gorical propositions.  The  classification  of  proposi- 
tons  into  disjunctive,  hypothetical,  and  categorical 

(222) 


CATEGORICAL   PROPOSITIONS 

is  said  to  be  made  from  the  standpoint  of  relation,  of 
the  relations,  that  is,  that  obtain  between  the  ele- 
ments that  enter  into  the  proposition.  It  is  quite 
obvious,  for  instance,  that  the  predicate  and  subject 
of  each  of  the  above  propositions  dealing  with  what, 
under  given  conditions,  can  be  predicated  of  a  par- 
ticular animal,  are  related  in  quite  distinct  ways. 
The  predicate  term  is  asserted  differently  in  each 
case,  and  it  is  this  difference  in  our  manner  of 
asserting  that  lies  at  the  foundation  of  the  distinc- 
tion we  make  between  disjunctive,  hypothetical,  and 
categorical  propositions.  The  form  of  assertion 
corresponds  to  a  real  element  in  the  knowledge  that 
an  assertion  claims.  We  have  shown  this  in  detail 
in  the  chapter  on  propositions.  Our  present  task 
is  to  study  the  various  kinds  of  propositions  and  the 
logical  problems  to  which  they  give  rise.  In  the 
present  chapter,  we  shall  consider  a  number  of  ques- 
tions which  relate  to  simple  predication  and  which 
throw  light  upon  the  nature  of  categorical  state- 
ments ;  in  the  next,  we  shall  consider  problems  con- 
nected with  the  other  forms  of  the  proposition. 

Classification  of  Categorical  Propositions.  The 
possibility  of  a  classification  of  categorical  proposi- 
tions, that  is,  propositions  which  predicate  P  of  S 
simply,  rests  upon  the  fact  that  unconditional  state- 
ments (1)  do  not  always,  but  sometimes  do,  apply 
to  a  determinate  part  of  the  subject-matter  of  such 
statements;  or  (2)  do  not  always,  but  sometimes  do, 
unite  the  predicate  with  the  subject  of  such  state- 
ments; or  (3)  do  not  always  express  the  same  de- 


224  A   TEXT-BOOK   OF  LOGIC 

gree  of  certainty.  We  shall  illustrate  each  of  these 
cases  in  the  order  in  which  they  have  been  named. 
As  an  illustration  of  the  first  case,  where  the  state- 
ment applies  to  an  indeterminate  part  of  the  subject- 
matter  of  the  statement,  let  us  take  'Not  all  men  are 
honest  who  say  they  are.'  This  is  a  proposition  in 
which  honesty  is  predicated  of  some  only  of  the  men 
who  declare  their  honesty.  As  an  illustration  of  the 
second  case,  where  the  statement  does  not  unite  the 
predicate  with  the  subject  of  the  proposition,  let  us 
take  the  illustration  just  used  and  observe  that  hon- 
esty is  denied  of  some  of  the  individuals  who  assure 
us  that  they  are  honest.  As  an  illustration  of  the 
third  case,  where  our  statements  express  different 
degrees  of  certainty,  let  us  take  the  following :  'He 
may  be  honest  though  poor;'  'He  is  honest  but 
poor;'  'He  must  be  honest.' 

The  three  characteristics  of  propositions  just 
mentioned  and  illustrated  are  so  constant,  and  they 
occur  in  such  a  wide  range  of  our  knowledge,  that 
early  in  the  history  of  logic  it  was  found  necessary 
to  distinguish  them  by  the  use  of  technical  terms, 
that  is,  by  terms  which  mean,  whenever  they  are 
used,  just  these  characteristics  of  propositions. 
Thus,  when  we  wish  to  call  attention  to  the  fact  that 
our  statements  do  or  do  not  apply  to  a  determinate 
part  of  the  subject-matter  of  the  proposition,  we 
are  said  to  be  dealing  with  the  proposition  from  the 
standpoint  of  its  Quantity.  When,  on  the  other 
hand,  we  wish  to  emphasise  the  fact  that  the  pred- 
icate does  or  does  not  belong  to  the  subject,  we  are 


CATEGORICAL   PROPOSITIONS  225 

said  to  be  dealing  with  the  proposition  from  the 
standpoint  of  its  Quality.  When,  thirdly,  we  wish 
to  distinguish  the  degree  of  certainty  that  attaches 
to  our  statements,  we  are  said  to  be  dealing  with 
the  proposition  from  the  standpoint  of  its  Modality. 
If  to  this  statement  we  now  add  what  was  said 
in  the  first  paragraph  of  the  present  chapter  about 
the  degrees  of  explicitness  in  predication  being  made 
from  the  standpoint  of  Relation,  we  have  before  us 
the  four  ways  in  which  propositions  may  be  class- 
ified. We  shall  now  write  down,  for  reference,  the 
classification  of  propositions  when  looked  at  from 
each  of  the  above-mentioned  points  of  view. 

RELATION 

Categorical 

Hypothetical 

Disjunctive 

QUANTITY  QUALITY 

Singular  Affirmative 

Universal  Negative 

Particular 
Indesignate 

MODALITY 

Assertoric 
Necessary 
Problematical 

Quantity  of  Propositions.  The  problem  of  the 
quantity  of  propositions  is  one  which  is  concerned 
with  the  question  whether  we  intend  our  statements 
to  be  true  of  a  determinate  or  indeterminate  part 
of  the  subject-matter  of  such  statements.  It  is,  for 

15 


226  A  TEXT-BOOK   OF  LOGIC 

example,  quite  clear  that  when  any  one  says,  'I  have 
seen  Paris/  he  is  ordinarily  understood  to  mean  that 
he  has  been  to  Paris,  and  visited  some  of  its  im- 
portant boulevards,  churches,  galleries,  etc.  No  one 
would  understand  him  to  mean  that  he  had  become 
acquainted  with  the  whole  of  Paris.  The  truth  of 
the  claim  to  have  seen  Paris  would  be  that  some 
unspecified  parts  of  Paris  had  been  visited.  Again, 
no  one  who  made  the  above  statement  would  ordi- 
narily wish  to  be  understood  that  he  had  a  thorough 
acquaintance  with  those  parts  of  Paris  which  had 
come  under  his  observation.  The  statement  is  in- 
tended to  claim  an  acquaintance,  such  as  it  is,  with 
certain  parts  of  the  French  capital.  From  these 
considerations,  it  is  quite  evident  that  the  statement, 
'I  have  seen  Paris/  leaves  undetermined  both  the 
range  and  the  thoroughness  of  the  observation  that 
is  claimed  by  the  statement.  Now,  although  a  great 
number  of  the  statements  we  make  about  even  the 
most  familiar  and  ordinary  events  of  life  are,  in  the 
sense  of  these  illustrations,  quite  undetermined,  we 
sometimes  make  statements  which  we  intend  to  be 
understood  with  no  such  limitation.  To  take  a  sim- 
ple illustration,  if  one  were  asked,  'What  is  the  most 
direct  route  from  Chicago  to  London?'  the  answer, 
if  one  were  given,  would  claim  to  be  determinately 
true  of  the  subject  of  the  inquiry,  either  of  a  speci- 
fied part  of  the  inquiry  or  of  the  whole  of  it.  For 
instance,  the  reply  might  take  this  form,  'Go  by  way 
of  the  New  York  Central  lines  to  New  York,  and 
then  inquire/  or  it  might  take  this  form,  'Go  to 


CATEGORICAL  PROPOSITIONS  227 

New  York,  and  then  take  passage  with  the  Cunard 
Line  to  London  via  Liverpool/  Let  us  take  another 
illustration.  A  mathematical  problem  is  an  inquiry 
of  a  definite  kind,  and  we  may  work  the  problem 
up  to  a  certain  point  quite  sure  that  all  the  steps 
we  have  taken  lead  us  toward  the  true  solution  of 
the  whole  problem.  We  may  or  we  may  not  be  able 
to  proceed  beyond  that  point.  The  fact  that  we  can- 
not, does  not  invalidate  the  claim  that  we  may  make 
of  having  solved  a  definite  part  of  the  problem.  That 
is  to  say,  if  the  answers  we  make  to  questions,  and 
the  statements  in  which  we  express  our  knowledge 
contain  in  them  a  distinct  reference  to  the  extent 
of  the  subject  covered  by  such  answers  and  state- 
ments, they  are  called  determinate  whether  th« 
whole  or  some  definite  part  of  the  whole  subject  has 
been  considered. 

We  have  seen  that  statements  may  be  deter- 
minate or  indeterminate  in  what  they  assert.  Our 
thought,  that  is  to  say,  may  refer  to  a  definitely 
specified  area  of  a  given  subject,  or  it  may  refer  to 
an  indefinitely  specified  area.  In  the  former  case, 
the  definitely  specified  area  may  be  either  the  whole, 
or  an  indicated  part  of  the  whole.  In  the  latter  case, 
we  cannot  tell  whether  the  knowledge  expressed  in 
the  statement  is  true  of  the  whole  or  of  only  a  part 
of  the  whole.  Now  these  distinctions  in  the  ordinary 
use  of  language  lie  at  the  foundation  of  the  logical 
consideration  of  propositions  from  the  standpoint  of 
quantity.  Hence,  the  question  of  the  quantity  of 
propositions  is  whether  what  a  statement  connotes 


228  A  TEXT-BOOK   OF  LOGIC 

is  true  of  a  specified  or  unspecified  part  of  what  its 
subject  denotes.  When,  consequently,  we  speak 
about  the  quantity  of  a  proposition,  we  must  be 
understood  to  be  interested  in  the  meaning  of  a  state- 
ment from  the  standpoint  of  the  number  of  the  ob- 
jects to  which  the  statement  applies.  It  is  obvious 
that  the  subject  terms  of  all  propositions  which  ex- 
press quantity  must  be  read  in  denotation. 

If  now  we  ask,  To  how  many  objects  can  we  in- 
tend our  statements  to  apply?  we  may  answer  to 
one,  to  more  than  one  but  less  than  all,  and  to  all. 
These  are  all  the  possible  cases,  and  they  afford  a 
clue  to  the  classification  of  propositions  from  the 
standpoint  of  quantity. 

The  Singular  Proposition.  When  a  statement  is 
made  of  one  specified  individual,  that  statement,  in 
logic,  is  said  to  be  a  singular  proposition.  'Hannibal 
was  a  great  Carthagenian  general'  is,  in  this  sense, 
a  singular  proposition.  It  is  a  proposition  that  ex- 
presses what  an  examination  of  a  single  instance  of 
the  genus  'general'  has  led  us  to  affirm.  This  is  not 
an  exceptional  case,  for  we  are  frequently  led,  in 
the  course  of  our  experience,  to  examine  single  ob- 
jects and  to  attempt  some  classification  of  them. 
The  child's  questions,  'What  is  this?'  'Who  made 
that?'  and  the  like  are  illustrations  of  the  impor- 
tance of  this  class  of  judgments  in  the  progress  of 
intelligence  and  the  advancement  of  knowledge. 
Singular  statements  are  concrete,  or  keep  us  in  close 
connection  with  what  is  concrete,  and  for  this  reason 
are  of  great  help  in  making  exact,  particular,  and 


CATEGORICAL  PROPOSITIONS  229 

precise  the  knowledge  that,  in  one  way  and  another, 
we  are  daily  acquiring.  The  examination  of  indi- 
vidual objects  is,  also,  a  large  part  of  the  work  of 
any  science,  and  much  of  the  knowledge  that  science 
has  consists  of  the  singular  judgments  it  is  able  to 
assert.  We  may  say  in  passing  that  the  student's 
danger  is  that  he  will  get  away  from  the  observation 
of  particular  things,  and  that  his  education  will 
force  him  to  premature  generalisation  in  which  a 
form  of  words  is  substituted  for  a  face  to  face 
acquaintance  with  the  facts  of  his  special  subjects 
of  study.  If  such  should  be  the  case,  it  is  hardly 
possible  that  he  will  appreciate  the  importance  of 
this  type  of  proposition. 

The  Universal  Proposition.  Another  class  of 
propositions  is  met  with  when  the  subject  terms  of 
such  propositions  are  general  instead  of  individual. 
'All  democratic  governments  tend  to  issue  in  despot- 
ism' is  a  statement  expressing  a  judgment  that  pur- 
ports to  be  based  upon  the  common  character  of  the 
individuals  that  the  general  term  signifies.  Greek, 
French,  British,  American,  etc.,  are  the  governments 
of  which  such  a  statement  is  held  to  be  true,  and 
yet  not  as  Greek,  French,  etc.,  but  as  democratic. 
Statements  of  this  kind  are  made  because  there  is 
conceived  to  be  a  necessary  connection  between  what 
the  predicate  and  subject  terms  connote,  and  they 
apply  to  all  individual  or  particular  instances  which 
possess  the  attributes  of  the  subject  term.  In  other 
words,  whenever  we  affirm  or  deny  of  each  of  a  total 
number  of  instances  the  meaning  that  attaches  to 


230  A  TEXT-BOOK   OF  LOGIC 

the  predicate  terms  of  propositions,  we  have  what, 
in  logic,  is  called  a  universal  proposition. 

Kinds  of  Universal  Proposition.  A  question  may 
arise  as  to  whether  there  is  any  logical  difference 
between  a  singular  and  a  universal  proposition,  since 
in  both  cases,  the  subject  term  must  be  understood 
to  be  distributed,  that  is,  to  apply  to  the  whole  num- 
ber of  the  instances  that  the  connotation  of  the  term 
implies.  There  can  be  no  objection  to  taking  these 
two  cases  as  illustrating  the  same  logical  principle, 
namely,  that  from  the  standpoint  of  their  quantity 
we  intend  our  statements  to  apply  to  all  the  in- 
stances, whether  to  a  specified  one  or  to  all,  to  which, 
in  the  nature  of  the  proposition,  the  subject  term  can 
apply.  The  singular  proposition  may  thus  be  taken 
as  a  particular  form  of  the  universal  proposition. 
Another  type  of  proposition  which,  like  the  singular 
proposition,  has  a  concrete  subject  term,  and  which, 
on  account  of  the  definiteness  of  its  denotation,  has 
to  be  interpreted  as  a  universal  proposition  may  be 
considered  in  this  connection.  For  example,  in  the 
proposition,  'A  part  is  always  less  than  the  whole/ 
a  part  is  a  perfectly  determined  idea  of  quantity 
from  the  logical  point  of  view,  and  the  proposition 
in  which  it  serves  as  a  subject  term  must,  therefore, 
be  treated  as  a  universal  proposition. 

The  Particular  Proposition.  Whenever  the  num- 
ber of  instances  denoted  by  the  subject  term  oi;  a 
proposition  is,  from  the  logical  standpoint,  unde- 
termined, we  are  said  to  have  a  particular  proposi- 
tion. The  question  for  us  to  bear  in  mind  in  decid- 


CATEGORICAL  PROPOSITIONS  231 

ing  the  quantity  of  a  proposition  is  simply  whether 
the  number  of  instances  of  the  kind  connoted  by  the 
subject  term  is  a  determined  number  or  not.  For 
example,  if  we  say  that  'Five  per  cent  of  all  college 
students  fail  in  their  work,'  it  is  clearly  not  meant 
that  we  know  the  exact  number  of  college  students, 
and  therefore  that  we  know  the  exact  number  who 
fail ;  the  statement,  if  it  is  true,  must  be  based  upon 
the  examination  of  large  numbers  of  students  work- 
ing under  a  great  variety  of  conditions,  and,  when 
so  based,  we  feel  warranted  in  saying,  even  with 
respect  to  those  students  who  have  not  had  an  oppor- 
tunity to  pass  or  to  fail  in  any  subject,  that  in  the 
period  covered  by  their  college  course  five  per  cent 
of  these  will  fail.  Now  what  we  wish  to  illustrate 
by  this  example  is  that  the  statement  is  a  universal 
one  because,  although  arithmetically  we  have  no 
idea  of  the  number  of  failing  students,  we  do  have 
in  the  subject  term  of  our  proposition,  'five  per  cent 
of  all  college  students,'  an  idea  logically  determined 
from  the  standpoint  of  its  quantity.  'Five  per  cent' 
is  just  as  definite  as  'this  one*  of  a  given  number, 
and  both  are  as  definite  as  'all'  of  the  given  number. 
But  if,  on  the  contrary,  in  the  absence  of  all  knowl- 
edge of  any  such  statistical  study  as  we  have  sup- 
posed, we  were  required  to  express  our  judgment 
as  to  the  number  of  failures  likely  to  be  incurred 
at  any  given  time,  we  could  not  logically  go  beyond 
the  statement  that  'Some  students  will  fail  in  their 
work.'  This  statement  is  true  of  an  undetermined 
number  of  students,  and  'some,'  as  a  sign  of  quantity 


232  A   TEXT-BOOK   OF  LOGIC 

in  propositions,  means  this.  The  propositions  that 
express  judgments  that  have  not  determined  the 
quantity  of  their  subject-matter  are  called  particular 
propositions. 

The  Indesignate  Proposition.  Whenever  we  ex- 
press judgments  of  quantity,  our  statements,  as  a 
rule,  bear  upon  their  face  some  definite  indication 
of  the  extent  of  their  subject  terms.  From  the 
standpoint  of  quantity,  all  our  statements  are  offered 
as  true  of  a  number  of  determined  or  undetermined 
individuals,  and  when  a  statement  is  made  without 
specifying  which  of  these  two  possibilities  is  meant, 
we  are  left  in  doubt  as  to  how  the  statement  is  to 
be  taken.  Now  sometimes  this  occurs.  The  popular 
wisdom  of  an  age  which  gets  itself  hardened  into 
groyerbs  is  frequently  defective  in  this  respect. 
'Dead  men  tell  no  tales,'  is  an  illustration  in  point. 
Are  we  to  understand  this  of  all  dead  men  or  only 
of  some  dead  men?  Is  there,  that  is,  a  necessary 
connection  between  being  dead  and  being  unable  to 
appear  as  a  witness  in  a  trial,  for  example;  or  are 
we  to  suppose  that  there  is  only  an  accidental  con- 
nection between  them,  and  that  in  some  cases  the 
testimony  of  dead  men  is  admissible?  'Virtue  is  to 
be  rewarded/  is  a  proposition  that  is  defective  in 
the  same  respect.  Are  we  to  understand  this  of  each 
and  all  the  virtues,  of  the  ordinary  virtues  of  our 
daily  life  as  well  as  of  the  more  heroic  virtues  that 
are  called  out  in  exceptional  circumstances;  or  are 
we  to  limit  the  statement  to  the  latter  class  of  cases  ? 
If  the  latter,  then  the  same  set  of  questions  recurs, 


CATEGORICAL   PROPOSITIONS  233 

and  we  should  wish  to  know  whether  a  reward  must 
be  attached  to  all  of  them  or  to  only  some  of  them. 
These  illustrations  are  sufficient  to  indicate  a  kind 
of  statement  we  sometimes  meet  with  even  in  com- 
mon life,  statements  that  are  quantitative  by  impli- 
cation but  are  not  explicitly  so.  How  are  we  to 
deal  with  them  logically?  Our  first  inclination  is  to 
receive  all  such  statements,  according  to  the  charac- 
ter of  their  subject-matter,  as  universal  or  par- 
ticular propositions.  But  if  it  is  remembered  that 
all  propositions  are  expressions  of  the  judgments  of 
the  person  who  states  the  proposition,  and  that  they 
are,  from  the  standpoint  of  the  person  who  hears 
them,  proposals  for  his  acceptance  or  rejection  in 
the  sense  in  which  they  are  made,  it  will  be  obvious 
that  we  are  not  allowed  to  interpret  these  statements 
in  any  sense  we  wish ;  our  business  is  to  understand 
them  in  the  sense  they  have  for  the  person  who 
makes  them.  But,  as  we  saw,  these  propositions 
create  a  doubt  that  is  based  upon  the  possibility  of 
understanding  the  statements  in  either  of  two  ways. 
Whenever  a  statement  raises  a  doubt  of  this  kind, 
a  doubt  that  may  be  resolved  by  accepting  either 
the  one  or  the  other  of  alternative  possibilities, 
without  indicating  which  alternative  is  to  be 
adopted,  it  is  called  an  indesignate  proposition.  An 
indesignate,  or  as  it  is  sometimes  called,  an  indefinite 
proposition  is  one  which  implies  the  existence  of  a 
determined  or  undetermined  number  of  individuals 
of  which  the  statement  is  offered  as  true,  but  which 
fails  to  state  explicitly  whether  it  is  made  of  the 


234  A  TEXT-BOOK  OF  LOGIC 

number  of  the  determined  or  of  the  undetermined 
instances. 

Quality  of  Propositions.  Our  study  in  a  previous 
chapter  has  shown  that  terms  always  intend  more 
than  they  express,  that  they  are  aspects  of  a  whole 
meaning  which  as  terms  they  do  not  fully  bring  out. 
We  have  also  learned  that  in  order  to  get  at  the 
full  meaning  of  any  term  we  must  find  it  functioning 
in  some  way  in  a  proposition.  It  is  only  in  a  prop- 
osition that  we  discover  the  full  meaning  of  a  term ; 
the  proposition  is  the  express  statement  of  the  whole 
meaning  within  which  the  meanings  of  terms  may 
properly  be  sought.  In  other  words,  it  is  the  way 
that  terms  function  in  propositions  that  gives  the 
key  to  the  meaning  of  the  proposition  and  of  the 
terms  themselves.  That  is  to  say,  we  have  to  inter- 
pret terms  from  the  standpoint  of  their  propositions 
and  proposition  from  the  standpoint  of  their  terms. 
The  reason  is  that  each  implies  the  other,  and 
neither  can  exist  alone. 

Coming  now  to  the  particular  problem  of  this 
section,  we  may  see,  in  the  light  of  what  has  just 
been  said,  that  terms  may  be  related  to  one  another 
in  propositions  in  one  or  the  other  of  two  ways,  in 
the  way  of  inclusion  or  of  exclusion.  The  fact  that 
terms  are  elements  of  the  meaning  expressed  by  the 
proposition,  is  indicated,  as  we  have  already  seen, 
by  the  copula.  The  copula,  we  said,  is  the  sign  of 
predication,  the  sign  that  S  and  P  are  to  be  taken 
in  the  way  required  by  the  whole  meaning  expressed 
in  the  proposition.  One  of  the  ways  in  which  prop- 


CATEGORICAL  PROPOSITIONS  235 

ositions  require  us  to  take  their  terms  is,  as  we  said, 
with  respect  to  whether  they  are  inclusive  or  exclu- 
sive of  each  other.  And  this  requirement  is  indi- 
cated by  the  copula,  which  according  as  it  has  or 
has  not  the  negative  particle  'not,'  distinguishes  for 
us  the  two  kinds  of  Quality  of  prepositional  state- 
ments. When  the  terms  are  inclusive,  this  is  indi- 
cated by  the  copula  'is'  or  'are;'  when  they  are  ex- 
clusive, by  the  copula  'is  not'  or  'are  not.'  The 
propositions  that  have  respectively  these  two  kinds 
of  copula  are  called  affirmative  and  negative  prop- 
ositions. Affirmative  and  negative  propositions, 
therefore,  are  statements  that  give  expression  to 
the  inclusive  and  exclusive  relationship  of  the  terms 
through  which  our  meanings  are  expressed. 

The  Affirmative  Proposition.  Affirmative  propo- 
sitions, formally  considered,  are  those  in  which  the 
copula  is  either  'is'  or  'are.'  From  the  standpoint 
of  the  character  of  the  thought  expressed  in  them, 
affirmative  propositions  may  be  defined  as  the  ex- 
pression of  our  positive  meanings.  By  a  positive 
meaning  we  understand  one  which  combines  in  a 
whole  content  of  thought  two  or  more  features  of 
the  object  thought  about.  Stated  differently,  a  pos- 
itive meaning  is  one  that  may  be  analysed  into  ele- 
ments each  of  which  expresses  some  feature  of  the 
meaning  which  the  proposition  as  a  whole  expresses. 
For  example,  the  meaning  of  the  proposition,  'All 
mammals  are  vertebrates'  is,  that  there  is  a  genus 
which,  when  looked  at  from  the  standpoint  of  an- 
atomy, must  be  described  as  a  vertebrate,  but  which 


236  A   TEXT-BOOK   OF   LOGIC 

if  looked  at  from  the  standpoint  of  physiology  must 
be  described  as  a  mammal.  Let  us  call  the  genus, 
or  the  whole  meaning  of  any  proposition,  SP.  Then 
our  positive  meaning,  SP,  may  be  analysed  into  S 
and  P,  and  these  terms  may  be  used  to  express  the 
intended  meaning  in  the  proposition  'S  is  P.'  To 
develop  the  significance  of  affirmative  predication 
further,  we  may  say  that  in  any  statement  of  the 
form  'S  is  P/  S  and  P  are  not  isolated  or  independent 
terms ;  S  is  not  merely  S,  nor  is  P  merely  P.  What 
the  proposition  affirms  is  that  the  S  that  is  P  is  an 
SP,  and  only  because  it  is  SP  can  we  say  that  it  is 
P.  But  P  can  be  predicated  of  S  only  if  it  also  is 
SP.  SP  underlies  both  terms,  and  gives  to  the  mean- 
ing that  the  proposition  'S  is  P'  expresses  its  posi- 
tive character. 

The  Negative  Proposition.  Negative  proposi- 
tions, formally  considered,  are  those  in  which  the 
copula  is  either  'is  not'  or  'are  not.'  Materially,  that 
is,  from  the  standpoint  of  the  character  of  the 
thought  expressed  in  them,  negative  propositions 
may  be  defined  as  the  expression  of  our  exclusive 
meanings.  By  a  negative  meaning,  therefore,  we 
understand  one  which  excludes  from  a  whole  con- 
tent of  thought  one  or  more  attributes  of  the  object 
thought  about,  either  because  it  does  not  at  all,  or 
because  it  does  not  now,  form  part  of  the  connotation 
of  the  whole  content  of  thought.  Stated  otherwise,  a 
negative  meaning  is  one  which  may  be  analysed  into 
elements  one  or  more  of  which  is  incompatible  with 
some  fact  or  truth  which  we  have  already  accepted. 


CATEGORICAL  PROPOSITIONS  237 

In  the  chapter  on  terms  we  discussed  negative 
meaning,  and  the  conditions  under  which  such  mean- 
ings arise  were  explained.  These  conditions  can  be 
reviewed  profitably  in  the  present  connection,  and 
they  will  be  found  to  throw  light  upon  the  general 
statement  in  the  present  parapragh  of  what  we 
understand  a  negative  meaning  to  be. 

We  shall  pass  on  to  other  aspects  of  the  same 
problem.  We  may  call  attention  then  to  the  fact 
that  the  predicate  terms  of  negative  propositions 
are  to  be  read  in  connotation.  The  reason  for  this 
is  that  logical  negation  expresses  incompatibility  in 
the  meanings  of  terms.  For  example,  'Apples  are- 
not  pears/  does  not  express  merely  the  perceptual 
differences  of  the  things  we  call  apples  and  the  things 
we  call  pears ;  what  the  proposition  means  is  that  if 
we  know  what  attributes  pears  have,  they  will  be 
found  not  to  be  the  attributes  which  apples  have. 
Now,  as  we  see  by  this  illustration,  the  difficulty 
about  negative  statements  is  that  they  seem  to  break 
the  connection  that,  as  we  said,  must  bind  S  and  P 
together  in  logical  propositions.  For  example,  we 
have  shown  that,  in  order  to  make  any  statement  of 
the  kind  S-P,  we  have  to  suppose  that  P  is  predi- 
cated of  S  on  the  ground  of  the  common  likeness  that 
underlies  the  differences  of  S  and  P.  It  is,  in  other 
words,  because  S  and  P  make  a  reference  to  the  same 
subject,  although  to  different  aspects  of  it,  that  pred- 
ication can  take  place  at  all.  Can  we  say  that  in  neg- 
ative propositions  there  is  the  same  identity  in  dif- 
ference that  is  the  ground  of  every  logical  state- 


238  A   TEXT-BOOK   OF   LOGIC 

ment?  It  would  seem  that  we  can;  only  the  differ- 
ences, in  this  case,  have  come  in  our  thought  to  be  a 
special  motive  for  the  judgment  we  assert.  In  other 
words,  in  affirmative  propositions  we  express  like- 
nesses amid  differences,  while  in  negative  proposi- 
tions we  express  differences  amid  likenesses.  The 
negative  proposition  has  this  characteristic  because, 
by  making  difference  the  motive  of  our  assertions, 
we  can  sometimes  best  conserve  the  unity  of  idea 
that  every  prepositional  statement  requires. 

The  Relation  of  Affirmative  and  Negative  Prop- 
ositions. A  study  of  the  relation  of  affirmative  and 
negative  statements  will  throw  still  further  light 
upon  the  meaning  of  negation.  In  affirmative  state- 
ments, thought  moves  between  two  extremes,  the 
extreme  of  tautology  on  the  one  hand,  and  the  ex- 
treme of  nonsense  on  the  other.  If  we  take  affirma- 
tion in  one  extreme  way,  we  can  only  express  iden- 
tical meanings,  'A  boy  is  a  boy/  and  this  is  taut- 
ology. If  we  take  affirmation  in  another  extreme 
way,  we  can  only  express  incompatible  meanings, 
'A  stove  is  a  gold  mine/  and  this  is  nonsense.  Now 
it  is  the  function  of  negation  to  save  us  from  mean- 
ingless —  tautological  or  nonsensical  —  assertions. 
For  instance,  the  case  of  tautology,  when  taken 
absolutely,  is  a  denial  of  the  minimum  of  difference 
which  must  exist  if  we  are  to  make  our  assertions 
significant.  Merely  to  predicate  an  object's  exist- 
ence of  itself,  or  to  affirm  a  meaning  of  itself,  is 
nothing  but  trifling.  If  we  should  mean  by  the 


CATEGORICAL  PROPOSITIONS  239 

predicate  only  what  we  mean  by  the  subject  of  a 
proposition,  we  should  state  in  the  whole  proposi- 
tion no  more  than  we  stated  in  either  of  its  terms. 
Thus,  'A  is  A'  has  exactly  the  meaning  of  A,  whether 
A  is  read  denotatively  in  both  terms,  or  connota- 
tively  in  both  terms.  If  A  is  A  is  a  significant  state- 
ment, we  must  at  least  read  A  denotatively  in  one 
term,  and  connotatively  in  the  other.  In  other 
words,  the  identity  which  unites  the  subject  and 
predicate  of  logical  propositions  must  not  go  to  the 
extreme  of  eliminating  all  differences  from  the 
meaning  which  logical  propositions  state.  The 
affirmative  proposition,  because  its  chief  interest 
is  in  identity,  is  particularly  open  to  the  danger  of 
overlooking  the  differences  that  make  the  subject 
and  predicate  of  such  propositions  distinct  terms. 
Now,  when  this  happens,  when  identity  usurps  the 
whole  functions  of  assertion,  we  can  be  saved  from 
the  fatuity  of  tautology  by  resorting  to  negation  as 
the  only  means  at  our  disposal  for  opening  the  way 
to  some  significant  statement.  Thus,  if  we  oppose 
any  tautology  with  a  denial,  the  burden  of  the  proof 
of  what  we  assert  is  thrust  upon  us,  and  this  con- 
sists in  showing  the  grounds  on  which  our  negation 
rests.  For  example,  if  we  deny  that  'A  boy  is  a  boy/ 
we  may  do  so  because,  as  we  may  point  out,  he  is 
also  a  son,  and  that  this  relationship  is  compatible 
with  the  fact  of  boyhood  from  which,  in  the  tauto- 
logical statement,  we  were  unable  to  get  away. 
Negation  serves,  in  such  a  case,  to  prevent  us  from 


240  A  TEXT-BOOK   OF  LOGIC 

standing  intellectually  stock-still;  and,  as  we  often 
find,  the  denial  of  truism  may  sometimes  be  the 
open  way  to  the  truth. 

The  other  extreme  to  which  affirmative  judg- 
ments may  lead  us  consists  in  the  development  of 
differences  to  such  an  extent  that  the  unity  of  the 
judgment  is  threatened  or  completely  destroyed. 
This  may  occur,  for  example,  when  the  material  of 
the  judgment  is  forced  to  render  so  many  predicates 
that  the  universe  of  discourse,  which  in  all  logical 
judgment  sets  the  limit  to  which  differences  can  be 
carried,  is  in  danger  of  being  superseded,  and  the 
qualities  which  the  material  may  have  in  other  uni- 
verses of  discourse  are  brought  in  to  satisfy  the 
demand  for  differences  which  has,  so  to  say,  got  out 
of  hand.  When,  for  example,  the  student  of  psy- 
chology speaks  of  auditory  sensations  being  brought 
in  over  the  auditory  nerve,  and  when  the  text-books 
of  physiology  speak  about  the  striated  muscles  being 
under  the  control  of  the  will,  there  is  a  confusion 
of  universes  of  discourse,  and  we  can  only  force  the 
statements  within  their  respective  bounds  again  by 
a  refusal  to  accept  them  as  significant  assertions. 
The  statements  are  incompatible  with  the  body  of 
knowledge  of  their  respective  sciences,  and  the  nega- 
tion is  in  each  case  in  the  interests  of  this  body  of 
accepted  knowledge. 

Exceptive  and  Exclusive  Propositions.  Whenever 
a  subject  of  discourse  is  qualified  by  such  words  as 
except,  only,  but,  unless,  alone,  none  but,  etc.,  it 
immediately  becomes  uncertain  to  what,  in  such 


CATEGORICAL   PROPOSITIONS  241 

cases,  the  predicate  applies.  For  example,  if  we  say, 
'All  free  persons  know  how  to  obey,'  it  is  quite  ob- 
vious that  we  are  predicating  'the  knowledge  of  how 
to  obey'  of  'the  persons  who  are  free.'  If,  however, 
we  were  to  say  'None  but  the  free  know  how  to  obey,' 
we  should  be  saying  something  quite  different,  al- 
though most  persons  would  understand  that  we  were 
still  predicating  'the  knowledge  of  how  to  obey'  of 
'the  persons  who  are  free.'  If,  again,  we  said,  'Only 
the  free  know  how  to  obey,'  it  might  be  asked 
whether  we  had  said  something  identical  with  one  of 
the  other  statements,  or  something  different  from 
both.  And,  further,  if  we  said,  'No  one  unless  he  is 
free  knows  how  to  obey,'  the  problem  would  become 
still  more  complicated. 

In  view  of  the  difficulties  of  interpretation  occa- 
sioned by  such  statements  as  those  to  which  atten- 
tion has  just  been  called,  it  is  customary  for  logic 
to  point  out  that  all  propositions  whose  subject 
terms  are  qualified  by  such  words  as  except,  only, 
but,  are  either  exceptive  or  exclusive  propositions. 
In  the  exceptive  and  the  exclusive  proposition  the 
subject  term  is  an  infinite  or  non-S  term,  because  all 
the  qualifying  words,  except,  but,  only,  etc.,  are 
understood  as  carrying  a  negative  signification. 
Examples  are :  'All  except  honor'  =  'All  that  is  not 
honour;'  'None  but  the  free'  =  'No  one  who  is  not 
free ;'  'Only  natives'  =  'No  one  who  is  not  a  native.' 
It  should  be  observed,  moreover,  that  exceptive  and 
exclusive  propositions  are  always  universal,  there 
are  no  particular  propositions  of  either  kind.  That 

16 


242  A  TEXT-BOOK   OF  LOGIC 

is  to  say,  the  subject  terms  of  these  propositions 
denote  always  a  determinate  number  of  individuals. 
But  while  the  exceptive  and  exclusive  propositions 
distribute  their  non-S  terms,  they  differ  from  each 
other  in  quality.  That  is  to  say,  all  propositions 
which  qualify  their  subjects  in  the  manner  indicated 
are  either  affirmative  or  negative.  In  the  light  of 
these  statements  we  may  consider  these  classes  of 
propositions  separately. 

The  exceptive  proposition  is  affirmative.    It  ha& 

the  genera]  form,  SaP.  Examples  are :  'All  planets 
except  Venus  and  Mercury  are  beyond  the  earth's 
orbit'  =  'Any  planet  that  is  not  Venus  or  Mercury 
is  beyond  the  earth's  orbit;'  'All  members  but  the 
Irish  voted  for  the  measure'  =  'All  the  members 
who  do  not  belong  to  the  Irish  party  voted  for  the 
measure/ 

In  an  exceptive  proposition  the  individuals  de- 
noted by  the  subject  term  are  determined  by  taking 
out  of  a  class  a  certain  number  of  individuals  to 
which  the  predicate  term  is  meant  not  to  apply.  It 
will  be  seen  that  if  the  part  of  the  class  to  which 
the  predicate  term  does  apply  is  to  be  distributed, 
the  part  taken  out  must  be  distributed  also.  What 
an  exceptive  proposition  says,  therefore,  is  that  a 
statement  is  true  of  that  part  of  a  class  which  re- 
mains when  stated  exceptions  to  it  are  definitely  re- 
moved. The  truth  of  such  a  statement  is  maintained 
of  everything  that  cannot  be  brought  under  the  ex- 
ception, that  is,  of  everything  that  is  not  the  speci- 
fied exception.  Consequently,  what  we  are  talking 


CATEGORICAL  PROPOSITIONS  243 

about,  in  an  exceptive  proposition,  is  anything, 
within  the  universe  of  discourse,  that  is  definitely 
non-S.  Thus,  if  a  circle  represents  a  universe  of 
discourse,  and  any  shaded  portion  of  it  the  excepted 
part,  which  may  be  called  S,  the  unshaded  part  will 
then  represent  the  denotation  of  the  subject  of 
predication,  that  is,  non-S.  The  exceptive  proposi- 
tion may  in  these  terms  be  represented  thus : 


SaP 

The  exclusive  proposition  is  negative.  It  has  the 
general  form,  SeP.  Examples  are :  'None  but  the 
brave  deserve  the  fair'  =  'No  one  who  is  not  brave 
deserves  the  fair;'  'Only  graduates  are  eligible' = 
'No  one  who  is  not  a  graduate  is  eligible.' 

The  exclusive  proposition  determines  its  subject 
term  in  the  same  way  as  the  exceptive  proposition, 
that  is,  by  taking  out  of  a  class  some  determinate 
number  of  individuals,  and  making  all  other  indi- 
viduals of  the  class  the  subject  of  predication.  Thus, 
if  S  be  the  excluded  individuals,  non-S  will  be  the 
subject  of  which  predication  takes  place.  But  since 
exclusive  propositions  are  negative,  the  individuals 
denoted  by  non-S  will  necessarily  have  qualities 
which  are  incompatible  with  their  possessing  those 
connoted  by  the  predicate  term;  incompatibility  of 
qualities  is  what  we  mean  by  negation.  Hence,  the 


244  A   TEXT-BOOK   OF   LOGIC 

exclusive  proposition  definitely  denies  P  of  every 
individual  which  does  not  have  the  qualities  also  of 
S ;  nothing  that  is  not  S  is  P.  If,  now,  we  represent 
any  excluded  part  of  a  class  by  the  shaded  portion 
of  a  circle,  the  exclusive  proposition  may  be  shown 
as  follows: 


SeP 

Compound  Propositions.  We  have  said  that  ex- 
ceptive and  exclusive  propositions  are  always  uni- 
versal. This  is  not  because  particular  propositions 
do  not  qualify  their  subject  terms  by  such  words  as 
only,  except,  etc.,  but  because  when  they  do,  they 
must  be  treated  as  compound  propositions.  By  a 
compound  proposition,  or,  as  the  older  logicians 
called  them,  exponible  propositions,  is  understood 
one  whose  meaning  requires  a  number  of  distinct 
propositions  for  its  complete  expression.  'Milton 
and  Dante  -wrote  religious  poetry  of  the  highest 
merit,'  is  a  simple  example.  The  meaning  of  the 
statement  obviously  is,  (a)  'Milton  wrote  religious 
poetry  of  the  highest  merit,'  and  (b)  'Dante  wrote 
religious  poetry  of  the  highest  merit.'  A  more  com- 
plex example  is,  'Men  who  are  honest  though  poor 
will  be  respected  and  helped.'  The  whole  sense  of 
this  can  be  expressed  in  the  two  statements  (a) 
'Poor  men  who  are  honest  will  be  respected,'  and 
(b)  'Poor  men  who  are  honest  will  be  helped.'  From 


CATEGORICAL   PROPOSITIONS  245 

these  examples  we  can  see  that  a  separate  expres- 
sion must  be  given  to  each  significant  idea  of  any 
complex  of  ideas. 

Bearing  in  mind  what  a  compound  proposition 
is,  let  us  turn  to  the  particular  propositions  which 
qualify  their  subject  terms  by  the  use  of  exclusive 
words  or  phrases.  These  propositions,  we  have  said, 
are  compound.  An  example  is,  'Some  only  who  en- 
list will  find  their  way  to  the  firing  line/  This 
obviously  cannot  mean,  'Some  who  do  not  enlist  will 
find  their  way  to  the  firing  line;'  that  is,  it  cannot 
be  treated  as  a  particular  exclusive  proposition. 
What  the  statement  means  is  (a)  'Some  who  enlist 
will  find  their  way  to  the  firing  line/  and  (b)  'Some 
who  enlist  will  not  find  their  way  to  the  firing  line.' 
The  following  must  also  be  treated  as  a  compound 
proposition,  'Excepting  a  few,  all  these  answers  are 
wrong.'  What  the  proposition  states  is  (a)  'Some 
of  these  answers  are  wrong,'  and  (b)  'Some  of  these 
answers  are  not  wrong.'  From  these  examples  it 
seems  obvious  that  whenever  we  qualify,  in  the  way 
indicated,  the  subject  terms  of  particular  proposi- 
tions, that  is,  whenever  'some'  is  used  in  its  exclusive 
sense,  the  proposition  must  be  resolved  into  two 
independent  particular  propositions,  the  one  affirm- 
ative and  the  other  negative.  In  the  light  of  these 
cases,  we  may  also  understand  why  the  particular 
proposition  which  has  no  such  exclusive  significance 
must  be  interpreted  as  either  affirmative  or  nega- 
tive, and  not  as  both.  For  instance,  'Not  all  for- 
eigners are  to  be  mistrusted'  means  'Some  foreigners 


246  A  TEXT-BOOK  OF  LOGIC 

are  not  to  be  mistrusted;'  and  if  any  one  were  to 
add  to  this  interpretation,  'Some  foreigners  are  to 
be  mistrusted/  he  would  be  going  beyond  what  is 
said  to  a  secondary  implication  of  what  is  said.  The 
latter  statement  is  doubtless  implied  in  the  original 
statement,  but  it  is  not  what  that  statement  asserts. 
Modality  of  Propositions.  The  knowledge  we 
have  of  different  subjects,  as  we  are  all  aware,  varies 
not  only  with  respect  to  the  nature  of  these  subjects 
themselves,  so  that  one  kind  of  knowledge  we  call 
history,  and  another  science,  and  another  phil- 
osophy, but  also  with  respect  to  the  degrees  of  our 
attainments  in  any  of  these  departments  of  knowl- 
edge, so  that  we  speak  about  these  several  subjects 
with  differing  degrees  of  confidence.  If,  for  ex- 
ample, the  student  has  diligently  pursued  the  study 
of  bacteriology  for  a  number  of  years  he  will  not 
only  know  a  great  deal  about  the  nature  and  condi- 
tions of  the  changes  that  microscopic  organisms 
produce  in  their  hosts,  but  he  will  have  developed, 
with  his  increasing  knowledge  of  the  subject,  a  cer- 
tain degree  of  confidence  in  his  ability  to  describe 
these  changes,  to  prepare  cultures,  and  to  do  many 
things  besides.  If  the  same  student  has  not  given 
a  good  deal  of  time  to  the  study  of  history,  he  will 
not  feel  the  same  degree  of  confidence  that  we  ob- 
served in  the  former  case,  if  he  were  asked  to  name, 
for  instance,  the  causes  that  produced  the  French 
Revolution.  There  are,  then,  different  degrees  of 
knowledge,  and  these  get  reflected  in  the  degrees  of 
confidence  with  which  we  express  what  we  know.  It 


CATEGORICAL  PROPOSITIONS  247 

is  this  fact  that  logic  refers  to  under  the  term  Mo- 
dality. The  meaning  of  this  statement  may  become 
clearer  if  it  is  pointed  out  that  the  term  modality 
does  not  refer  to  any  uncertainty  that  may  exist 
as  to  the  nature  and  relations  of  the  object  of  judg- 
ment, but  only  to  the  degrees  of  certainty  of  our 
knowledge  of  the  object.  Modality,  that  is  to  say,  is 
a  logical  distinction;  it  characterises  our  thoughts 
about  things,  and  not  the  things  themselves.  Whether 
there  is  any  uncertainty  in  things  themselves  can- 
not be  discussed  in  an  elementary  logic,  but  that 
varying  degrees  of  certainty  and  uncertainty  attach 
to  our  knowledge  of  things  is  a  fact  well  known  to 
all. 

It  is  usual,  in  logic,  to  distinguish  three  degrees 
of  certainty,  and  to  throw  these  into  typical  preposi- 
tional forms  when  we  wish  to  express  the  modality 
of  our  thought.  The  propositions  which  set  forth 
the  modality  of  our  judgments  are  called  assertoric, 
problematic  and  apodeictic.  We  may  state  what  is 
to  be  understood  by  each  of  these  in  order. 

The  Assertoric  Proposition.  An  assertoric  prop- 
osition has  the  same  form  as  the  affirmative  cate- 
gorical proposition,  and  yet  is  not  to  be  understood 
in  the  same  way.  The  categorical  proposition  ex- 
presses the  way  that  S  and  P  are  related  in  the  uni- 
verse of  discourse  that  defines  the  limits  of  the  judg- 
ing activity,  and,  therefore,  relates  to  the  matter  of 
the  judgment.  The  assertoric  judgment,  on  the 
other  hand,  expresses  one  of  the  degrees  of  certainty 
of  our  knowledge  about  the  subject-matter.  For 


248  A  TEXT-BOOK   OF  LOGIC 

example,  if  we  were  to  say,  'All  men  are  biped/  we 
should  most  likely  be  understood  to  express  a  judg- 
ment founded  upon  common  observation,  and  that 
is  what  the  categorical  proposition  of  the  form, 
*S  is  P,'  usually  does.  If,  however,  with  respect  to 
this  judgment,  we  were  asked,  'What  makes  you 
think  so?'  we  should  possibly  hunt  around  the  var- 
ious corners  of  our  knowledge  for  a  reason  for  think- 
ing that  walking  on  two  feet  is  characteristic  of  all 
men.  If  from  such  an  excursion  and  search  we 
were  to  return  without  anything  that  threw  light 
upon  the  question,  we  should  probably  reply,  'I  don't 
know,  but  he  is  a  biped.'  We  should,  that  is,  assert 
with  emphasis  our  original  statement,  and  thereby 
express  our  confidence  in  the  correctness  of  the 
original  statement.  What,  therefore,  an  assertoric 
proposition  does  is  to  assert  that  S  is  actually  P,  or, 
stated  another  way,  that  'S  is  P'  is  actual,  whether 
any  reason,  other  than  perception  or  memory  sup- 
plies, can  be  given  or  not. 

The  Problematic  Proposition.  A  problematic 
proposition  states  that  'S  is  possibly  P,'  or  the  fact 
expressed  by  'S  is  P'  is  possible.  The  possibility 
does  not  imply  any  uncertainty  in  the  fact  expressed, 
but  only  an  uncertainty  in  the  state  of  our  knowl- 
edge about  the  fact,  an  uncertainty  that  makes  it 
impossible  for  us  to  state  with  any  higher  degree 
of  confidence  the  correctness  of  what  we  say.  For 
example,  the  student  who  is  reading  this  section  of 
logic  may  say,  'My  understanding  of  the  subject  is 
possibly  correct.'  What  he  means  by  this  is  not 


CATEGORICAL  PROPOSITIONS  249 

that  his  understanding  may  be  described  as  possibly 
correct,  for  there  is  no  such  thing  as  'possibly  cor- 
rect,' but  that  the  statement,  'My  understanding  of 
this  subject  is  correct'  is  a  possibility  in  his  own 
case.  If  we  take  a  simpler  case  this  will  become 
clear.  'The  rose  is  possibly  white'  does  not  mean 
that  'possibly  white'  is  the  colour  that  the  rose  has, 
for  there  is  no  such  colour.  We  are  to  understand 
the  adverb  to  qualify  not  any  part  of  the  statement, 
but  the  whole  assertion  —  'The  rose  is  white,'  and 
then,  as  in  the  other  case,  this  statement  expresses 
a  possibility. 

If  this  is  the  view  that  we  must  adopt  of  prob- 
lematic propositions,  what,  we  may  ask,  is  the 
ground  of  the  implied  uncertainty?  The  uncertainty 
is  not  due,  as  in  assertoric  propositions,  to  the  fact 
that  there  are  no  discoverable  reasons  for  the  state- 
ment, but  that  the  discovered  grounds  of  the  state- 
ment are  of  such  a  nature  that  we  can  never  be  sure 
that  we  have  all  the  elements  necessary  to  give  our 
statement  any  higher  degree  of  certainty.  To  illus- 
trate :  the  student's  understanding  of  this  paragraph 
must,  as  we  know,  be  correct  or  incorrect,  just  as  the 
rose  must  have  any  one  or  other  of  the  colours  that 
belong  to  the  species  rose.  If  we  have  not  seen  the 
rose  in  question,  we  know  only  that  it  is  either  red 
or  pink  or  white  or  yellow,  and  because  it  may  be 
something  else  than  what  we  assert,  we  merely  say 
that  it  is  possibly  white.  So  in  the  case  of  the  stu- 
dent: his  understanding  is  either  correct  or  incor- 
rect, but  because  the  alternatives  have  not  been  de- 


250  A  TEXT-BOOK   OF  LOGIC 

termined  with  respect  to  the  case  in  hand,  he  can 
only  say  that  his  understanding  of  the  paragraph 
is  possibly  correct.  A  possibility,  therefore,  means 
the  presence  of  alternatives  between  which  no 
ground  of  decision  has  as  yet  been  found. 

Judgments  which  involve  human  volition  as  one 
of  their  factors,  even  when  these  judgments  involve 
no  alternatives,  are  said  to  be  problematic.  For 
example,  'I  may  go  tomorrow,'  means  that  'I  will 
go  tomorrow'  is  the  statement  of  a  fact  that  is  pos- 
sible. Here  we  have  not  a  series  of  alternatives  as 
the  ground  of  the  uncertainty  of  the  judgment,  but 
the  absence  of  some  of  the  factors  that  are  neces- 
sary for  a  more  positive  statement.  All  actions  that 
depend  on  human  volition  are  said  to  be  contingent, 
and  therefore  a  judgment  that  involves  volition  as 
one  of  its  factors  must  always  be  problematic. 

The  Apodeictic  Proposition.  Apodeictic  judg- 
ments are  necessary :  'S  must  be  P.'  There  exists, 
in  this  case,  necessary  grounds  for  the  matter  of 
fact  judged.  'S  is  P'  is  necessary.  Necessity  is  a 
word  that  must  be  used  carefully.  This  is  obvious 
if  we  call  attention  to  the  different  kinds  of  neces- 
sity upon  which  our  apodeictic  statements  depend. 
Mathematical  statements,  although  not  expressed  in 
the  form  of  apodeictic  propositions,  are  necessary. 
For  example,  'A  straight  line  is  the  shortest  dis- 
tance between  two  points.'  What  the  mathematician 
understands  by  this  statement  is  that  the  shortest 
distance  between  two  points  must  be  what  we  mean 
by  a  straight  line.  The  idea  of  a  straight  line 


CATEGORICAL  PROPOSITIONS  251 

carries  that  meaning  necessarily.  Here,  then,  we 
have  necessity '  resting  upon  the  clearness  with 
which  an  idea  itself  is  conceived  or  apprehended, 
and  not  on  anything  else.  Another  class  of  neces- 
sity is  met  with  when  our  judgments  rest  upon 
other  judgments  which  may  or  may  not  be  neces- 
sary. For  example,  the  equality  of  triangles  on 
equal  bases  and  between  the  same  parallels  is  a 
case  of  necessity  resting  upon  grounds  that  are 
themselves  necessary.  In  all  truly  apodeictic  judg- 
ments there  is  presumed  to  be  an  inter-connection 
of  fact  that  makes  the  fact  asserted  by  the  judg- 
ment necessary. 

REFERENCES 

B.  Bosanquet,  The  Essentials  of  Logic,  Lect.  VII. 

J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Chs.  VII.,  VIII. 
W.  S.  Jevons,  Lessons  in  Logic,  Lesson  VIII. 
J.  N.  Keynes,  Formal  Logic,  2d  Edition,  Part  II.,  Ch.  I. 
S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  III.,  Part  I. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Ch.  V. 

ADVANCED 

J.  M.  Baldwin,  Thought  and  Things,  Vol.  II.,  Part  II.,  Ch. 

VIII. 

B.  Bosanquet,  Logic,  Vol.  I.,  Book  I.,  Chs.  II-IX. 
F.  H.  Bradley,  The  Principles  of  Logic,  Book  I.,   Chs.  VI- 

VIII. 

R.  W.  B.  Gibson,  The  Problem  of  Logic,  Ch.  VII. 
H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Ch.  VIII. 
H.  Lotze,  Logic,  Vol.  I.,  Ch.,  II. 
J.  S.  Mill,  A  System  of  Logic,  Book  L,  Ch.  IV. 
F.  C.  S.  Schiller,  Formal  Logic,  Ch.  XI. 


252  A  TEXT-BOOK   OF  LOGIC 

C.  Sigwart,  Logic,  Chs.  IV-VI. 

J.  Welton,  A  Manual  of  Logic,  Book  II.,  Ch.  I. 

QUESTIONS 

1.  What  is  the  ground  of  the  difference  between  the  three 
types  of  propositions? 

2.  Describe*  the  four  main  classes  of  categorical  proposi- 
tions. 

3.  Explain    and    illustrate   what   you    understand    by   the 
quantity  of  propositions. 

4.  What  is   a  singular  proposition?     Illustrate  and   state 
its  importance. 

5.  What  is  a  universal  proposition? 

6.  What  is  the  relation  of  the  singular  and  universal  prop- 
osition? 

7.  What  is  a  particular  proposition,  and  with  what  form 
of  universal  proposition  is  it  most  likely  to  be  confused? 

8.  Describe  and  illustrate  the  indesignate  proposition. 

9.  What  do  you  understand  by  the  quality  of  propositions? 

10.  What  are  the  characteristics  of  affirmative  propositions? 

11.  Describe  and  illustrate  a  negative  proposition. 

12.  Why  must  the  predicate  of  negative  propositions  be  read 
connotatively? 

13.  What  is  the  relation  of  tautology  to  affirmative  state- 
ments? 

14.  In  what  way  can  tautological  statements  be  overcome? 

15.  What  is  the  logical  status  of  nonsense? 

16.  In  what  respects  are  exceptive  and  exclusive  proposi- 
tions alike? 

17.  State    and    illustrate   the    characteristics    of   exceptive 
propositions. 

18.  What  is  an  exclusive  proposition?    Illustrate. 

19.  Why   are   there    no    particular    exceptive    or    exclusive 
propositions? 

20.  What  is  a  compound  proposition?    By  what  other  name 
is  it  known?    Illustrate. 

21.  Explain  what  is  meant  by  the  modality  of  propositions. 


CATEGORICAL   PROPOSITIONS  253 

22.  What   is    an    assertoric    proposition,    and    how   does   it 
differ  from  the  categorical  proposition? 

23.  Explain  and  illustrate  the  problematic  proposition. 

24.  How  will  you  classify  judgments  which  involve  human 
volition  as  one  of  its  factors? 

25.  Describe  and  illustrate  the  apodeictic  proposition. 

EXERCISES. 

1.  Write  in  parallel  columns  a  list  of  six  singular  and  six 
general  propositions,   and   be  ready  to  defend  the   as- 
signed character  of  these  propositions. 

2.  What  kind  of  proposition  is,  'Water  is  a  liquid  composed 
of  one  part  oxygen  and  two  parts  hydrogen.'     Give  rea- 
sons for  your  answer. 

3.  What  is  the  distribution  of  the  predicate  term  of  the 
proposition  in  the  preceding  question? 

4.  Give  three  illustrations  of  indesignate  propositions. 

5.  What  kind  of  proposition  is,  'Oxygen  is  necessary  for 
the  maintenance  of  life'? 

6.  Without  using  the  sign  of  quantity  'some,'  give  three 
illustrations  of  particular  propositions. 

7.  Classify  the  following  propositions  from  the  standpoint 
of  quantity,  and  in  each  case  state  the  reason  for  your 
classification : 

(1)  Each  of  the  hunters  shot  a  bird. 

(2)  Rivers  generally  run  into  the  sea. 

(3)  Blood  is  thicker  than  water. 

(4)  Afflictions  are  often  salutary. 

(5)  Can  the  leopard  change  his  spots? 

(6)  Veteran  soldiers  are  the  steadiest  in  battle. 

(7)  Suspicion  ever  haunts  the  guilty  mind. 

(8)  Knowledge  is  power. 

(9)  The  longest  road  has  an  end. 

(10)  Almost  any  Turk  hates  a  Greek. 

(11)  Philosophy  and  Psychology  are  necesary  to  a  well- 
rounded  education. 

(12)  Only  those  who  know  are  in  the  end  to  be  trusted. 


254  A  TEXT-BOOK   OF  LOGIC 

8.  Illustrate  how  affirmative  statements  can  be  made  either 
tautological  or  nonsensical. 

9.  Write  a  complete  account  of  how  one  negative   state- 
ment of  your  own  selection  may  conceivably  have  come 
to  be  made. 

10.  Write  a  list  of  three  assertoric  propositions,  and  show 
how   they  differ   from   affirmative   categorical   proposi- 
tions. 

11.  Explain  the  problematic  nature  of  six  propositions  of 
your  own  selection. 

12.  Write  a  list  of  three  apodeictic  propositions. 


CHAPTER  IX 

IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS 

Relation  of  Quantity  and  Quality  in  Categorical 
Propositions.  When  the  subject  term  of  a  proposi- 
tion is  read  in  denotation,  it  refers  to  a  determined 
or  undetermined  number  of  individuals,  and  when 
the  predicate  term  of  a  proposition  is  read  in  conno- 
tation, it  either  affirms  or  denies  the  meaning  of  the 
predicate  term  of  the  individuals  denoted  by  the 
subject  term.  Now,  since  every  proposition  under- 
takes to  set  forth  both  these  relations  of  its  subject- 
matter,  there  are  no  propositions  which  do  not  pos- 
sess both  quantity  and  quality. 

From  the  standpoint  of  their  quantity,  categor- 
ical propositions,  as  we  have  seen,  are  either  univer- 
sal or  particular;  that  is,  logical  statements  are 
always  about  a  determinate  or  indeterminate  part 
of  the  subject-matter  of  such  statements.  From  the 
standpoint  of  their  quality,  categorical  propositions 
are  either  affirmative  or  negative;  that  is,  logical 
statements  either  affirm  or  deny  an  attribute  of 
some  determinate  or  indeterminate  part  of  their 
subject.  Combined  in  a  single  statement,  these 
facts  and  relations  may  be  expressed  thus :  Propo- 
sitions with  distributed,  as  also  those  with  undis- 
tributed, subject  terms  are  either  affirmative  or 
negative  in  quality.  There  are  thus  four  proposi- 
tions, —  the  universal  affirmative,  the  universal  neg- 

(255) 


256  A  TEXT-BOOK   OF  LOGIC 

ative,  the  particular  affirmative,  the  particular  neg- 
ative, —  whose  relations  may  be  shown  in  a  table 
as  follows: 

QUANTIT\  QUALITY 

{a.  Affirmative 

b.  Negative 
Propositions   , 

f  a.  Affirmative 
Particular 

[  b.  Negative 

This  table  may  be  read:  Propositions  may  be 
universal  in  quantity  and  either  affirmative  or  neg- 
ative in  quality ;  or  they  may  be  particular  in  quan- 
tity and  either  affirmative  or  negative  in  quality. 

Structural  Formulae  indicating  the  Quantity  and 
Quality  of  Propositions.  The  problems  that  we  are 
to  study  in  this  chapter  arise  out  of  the  fact  that 
propositions  involve  the  relations  both  of  quantity 
and  quality.  Whatever  else  the  student  can  or  can- 
not do  with  a  proposition,  it  is  of  fundamental  im- 
portance that  he  should  be  able  to  determine  it  both 
with  respect  to  its  quantity,  and  also  with  respect  to 
its  quality.  The  student  will  find  ic  entirely  possible 
to  acquire  a  considerable  degree  of  facility  in  thus 
determining  the  propositions  that  come  before  him 
for  study ;  and,  moreover,  a  little  additional  industry 
in  this  matter  will  carry  him  a  long  way  toward 
overcoming  some  of  the  difficulties  that  he  will  meet 
farther  along  the  road.  When  he  has  become  prac- 
tically familiar  with  these  distinctions,  it  will  be  a 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS  257 

great  convenience  if,  for  the  propositions  that  em- 
body these  distinctions,  he  write  formulae  which 
indicate  their  quantity  and  quality.  The  value  of 
such  formulae  is  that  they  enable  one  to  deal  only 
with  the  essential  aspects  of  assertions,  and  they 
shorten  the  method  of  referring  to  these  essential 
aspects.  Like  any  other  formulae,  those  used  in 
logic  are  more  or  less  arbitrary  devices,  and  are  to 
be  justified  by  their  usefulness.  They  are  in  no 
sense  a  substitute  for  the  logical  facts  and  relations 
which  they  are  merely  the  means  of  expressing. 

Our  first  aim  then  will  be  to  distinguish  by  a 
convenient  symbol  the  four  typical  propositions 
mentioned  above.  This  is  usually  done  by  taking 
the  first  vowel  of  the  Latin  word  for  affirmation 
(affirmo),  and  the  first  vowel  of  the  Latin  word 
for  negation  (nego)  to  denote  the  universal  propo- 
sition of  the  quality  indicated  by  the  word,  and  the 
second  vowel  of  each  word  in  like  manner  to  indi- 
cate the  respective  particular  propositions.  Thus, 
A  and  E,  the  first  vowels  in  the  words  affirmo  and 
nego,  are  used  to  indicate  the  universal  affirmative 
and  universal  negative  propositions  respectively. 
The  second  vowels  in  the  same  Latin  words  are  I 
and  0,  and  these  are  used  to  indicate  respectively 
the  particular  affirmative  and  particular  negative 
propositions.  If,  now,  we  add  these  facts  to  the 
table  printed  above,  we  have  the  following  result : 


17 


258  A  TEXT-BOOK   OF  LOGIC 

QUANTITY  QUALITY  SYMBOL 

f  a.  Affirmative  A 
1.     Universal 

[  b.  Negative  E 
Propositions  - 

{a.  Affirmative  I 

b.  Negative  O 

Whenever,  in  the  foregoing  pages,  we  have  had 
occasion  to  refer  to  the  structure  of  a  proposition 
without  respect  to  its  quantity,  we  have  written  'S 
is  P,'  or  'S  is-not  P.'  Whenever  we  have  wished  to 
indicate  the  quantity  as  well  as  the  quality  of  prop- 
ositions, we  have  written  'All  S  is  P,'  'No  S  is  P,' 
'Some  S  is  P,'  'Some  S  is-not  P.'  This,  however,  is 
too  cumbersome  a  method  when  a  simpler  one  is 
possible.  And,  therefore,  logicians  have  adopted 
the  device  of  substituting  for  the  copula  in  proposi- 
tions of  the  general  form  S-P,  one  or  other  of  the 
four  vowels  by  which  the  four  kinds  of  categorical 
propositions  are  distinguished.  In  this  way  we  get 
the  following  structural  formulae:  SaP,  SeP,  SiP, 
SoP,  which  are  read  'All  S  is  P/  'No  S  is  P,'  'Some 
S  is  P/  'Some  S  is-not  P.' 

The  following  table  summarises  the  important 
facts : 

QUANTITY  AND  STRUCTURAL 

QUALITY  FORMULA  READ 

f  1.  Universal  Affirmative  SaP  All    S  is  P 

2.  Universal  Negative  SeP  No    S  is  P 
Propositions  <j 

13.  Particulare  Affirmative  S&P  Some  S  is,P 

4.  Particular  Affirmative  S$P  Some 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS  259 

This  table  should  be  read :  Propositions  as  to  their 
quantity  and  quality  may  be  either  universal  affirm- 
ative, with  the  structural  formula  SaP  which 
is  read  'All  S  is  P;'  or  universal  negative,  with 
the  structural  formula  SeP  which  is  read  'No  S  is 
P;'  or  particular  affirmative,  with  the  structural 
formula  SiP  which  is  read  'Some  S  is  P;'  or  par- 
ticular negative  with  the  structural  formula  SoP 
which  is  read  'Some  S  is-not  P.' 

Distribution  of  the  Terms  of  the  Four  Categorical 
Propositions.  The  logical  meaning  of  distribution  has 
been  discussed  in  the  chapter  on  terms,  and  we  met 
the  same  question  again  when  considering  the  quan- 
tity of  propositions.  We  need,  therefore,  only  repeat 
what  was  shown  more  at  length  above,  that  by  dis- 
tribution is  meant  the  width  or  extent  of  the  mean- 
ing expressed  in  a  proposition.  We  have  seen,  for 
example,  that  from  the  standpoint  of  quantity  the 
subject  terms  of  universal  propositions  are  dis- 
tributed ;  they  denote  a  determinate  number  of  indi- 
viduals, each  of  which  possesses,  or  does  not  possess, 
in  addition  to  the  qualities  connoted  by  the  term 
itself,  those  qualities  also  that  are  connoted  by  the 
predicate  term  of  such  propositions.  From  the  same 
standpoint,  the  subject  terms  of  particular  proposi- 
tions, on  the  other  hand,  are  undistributed;  they 
refer  to  an  indeterminate  number  of  denoted  indi- 
viduals. 

We  have  now  to  ask  what  influence  the  quality 
of  propositions  has  upon  the  distribution  of  pred- 
icate terms.  And  first  let  us  consider  affirmative 


260  A  TEXT-BOOK   OF  LOGIC 

propositions.  In  affirmative  propositions  we  pred- 
icate the  attribute  connoted  by  P  of  the  object  or 
objects  denoted  by  S.  So  far  as  they  are  affirmative, 
propositions  do  not  enable  us  to  say  whether  there 
are  any  objects,  other  than  those  denoted  by  the 
subject  term,  to  which  the  attributes  of  the  pred- 
icate term  apply.  Sometimes  there  are  such  objects ; 
as,  for  example,  The  cat  is  a  domesticated  animal/ 
for,  as  we  know,  there  are  other  domesticated  ani- 
mals than  cats.  Sometimes  there  are  not,  as,  for 
example,  Terception  is  the  consciousness  of  par- 
ticular material  objects  present  to  sense/  for  there 
are  no  other  objects  to  which  such  a  description  can 
apply  except  perception.  In  view  of  these  facts,  it 
is  obvious  that,  from  the  form  of  the  proposition,  it 
is  quite  impossible  to  determine  whether  universal 
affirmative  statements  are  to  be  understood  in  the 
one  or  the  other  of  the  ways  just  indicated ;  whether, 
that  is  to  say,  they  may  be  said  to  have  distributed 
or  undistributed  predicate  terms.  On  account  of 
this  uncertainty,  it  is  customary,  in  the  absence  of 
any  reason  connected  with  the  subject  matter  to  the 
contrary,  to  regard  the  predicate  terms  of  such 
propositions  as  undistributed. 

The  predicate  terms  of  negative  propositions,  on 
the  other  hand,  are  distributed.  The  reason  for  this 
is  that  it  is  only  when  every  object  which  can  be 
included  in  the  denotation  of  the  predicate  term  is 
excluded  from  the  subject  that  the  proposition  can 
have  a  negative  force  at  all.  For  if  all  P's  were 
not  definitely  separated  from  the  S,  some  P's  might 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS  261 

be  included  in  it,  and  this  would  not  express  the 
meaning  of  negation.  Negation,  as  we  have  seen, 
has  always  a  definitely  exclusive  force.  And  this  is 
true  of  negative  propositions  irrespective  of  their 
quantity ;  it  is  true  of  the  particular  as  well  as  of  the 
universal  negative  proposition.  Of  the  universal 
proposition,  SeP,  this  is  easily  seen  to  hold.  For 
if  'No  S's  are  P's'  has  any  meaning  at  all,  it  must 
surely  mean  that  not  any  of  the  S's  are  any  of  the 
P's.  That  is  to  say,  of  none  of  the  objects  that  have 
the  qualities  connoted  by  S  can  we  affirm  that  they 
have  also  the  qualities  connoted  by  P.  If  that  is 
true,  no  P's  are  any  of  the  S's.  But  the  same  thing 
can  be  shown  also  of  the  particular  proposition,  SoP. 
'Some  S's  are-not  P's'  must  mean  that  none  of  the 
objects  denoted  by  S  has  the  qualities  connoted  by 
P ;  and  that  is  equivalent  to  saying  that  none  of  these 
S's  are  at  the  same  time  P's.  The  objects  denoted 
by  P,  if  there  are  any,  are  entirely  excluded  from 
the  number  of  objects  referred  to  by  S.  If,  in  this 
case,  any  difficulty  arises  on  account  of  the  un- 
distributed nature  of  the  subject  term,  we  can  only 
say  that  the  meaning  of  the  proposition  is  that  there 
are  at  least  some  unspecified  instances  of  S's  that  do 
not  have  the  characteristics  of  P;  and  that  if,  as 
may  or  may  not  happen,  you  discover  any  S's  that 
do  have  these  characteristics,  then  they  are  not  the 
S's  to  which  the  proposition  refers.  It  follows, 
from  these  considerations,  that  the  predicate  terms 
of  all  negative  propositions  are  distributed. 


262 


A   TEXT-BOOK   OF  LOGIC 


We  may  summarise  the  foregoing  discussion  in 
the  four  following  statements: 

1.  The  subject  terms  of  propositions  that  are 
universal  in  quantity  are  distributed. 

2.  The  subject  terms  of  propositions  that  are 
particular  in  quantity  are  undistributed. 

3.  The  predicate  terms  of  propositions  that  are 
affirmative  in  quality  are  undistributed. 

4.  The  predicate  terms  of  propositions  that  are 
negative  in  quality  are  distributed. 

Thorough  familiarity  with  the  distribution  of 
the  terms  of  categorical  propositions  is  so  essential 
to  the  student's  understanding  of  what  follows  that 
he  is  urged  to  master  the  subject  at  this  point  of  his 
studies.  Because  of  the  importance  of  the  subject, 
and  as  a  further  aid  to  its  mastery,  we  add  the  fol- 
lowing tables  each  of  which  represents  the  facts 
contained  in  the  foregoing  summary.  The  letters 
D  and  U  stand  for  distributed  and  undistributed 
respectively : 

PROPOSITION 


STANDPOINT 


Quantity 


f 
SUBJECT 

D 

a 

> 

PREDICATE 

U 

D 

e 

D 

U 

i 

U 

U 

0 

D 

STANDPOINT 


Quality 


This  table  may  be  read  as  follows :    From  the  stand- 
point of  quantity,  the  subject  term  of  an  A  or  uni- 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS  263 

versal  affirmative  proposition  is  distributed;  from 
the  standpoint  of  quality,  the  predicate  term  of  an 
A  or  universal  affirmative  proposition  is  undistrib- 
uted, etc. 

Another  way  of  stating  the  same  set  of  facts  is 
to  say  that  the  subject  terms  of  propositions  that 
are  universal  in  quantity  are  distributed,  and  those 
that  are  particular  in  quantity  are  undistributed; 
that  the  predicate  terms  of  propositions  that  are 
affirmative  in  quality  are  undistributed,  and  those 
that  are  negative  in  quality  are  distributed.  The 
following  table  represents  these  facts : 

QUANTITY  DISTRIBUTION 

(Universal  D 

Subject  terms       J 

[Particular  ^U 

QUALITY  DISTRIBUTION 

f  Affirmative  U 

Predicate  terms    1 

[Negative  D 

Meaning  and  Classes  of  Implication.  The  group 
of  topics  that  are  now  to  be  discussed,  and  to  which 
the  preceding  pages  are  an  introduction,  is  by  some 
writers  brought  together  under  the  title  of  'imme- 
diate inferences/  and  by  others  under  the  title  'in- 
terpretation of  propositions/  The  objection  that  is 
usually  urged  against  'immediate  inferences'  is  that 
an  inference  always  involves  the  use  of  a  middle 
term,  and  is  therefore  mediate;  and,  consequently, 


264  A  TEXT-BOOK   OF  LOGIC 

that  it  is  a  contradiction  to  speak  of  'immediate'  in- 
ferences. The  objection  that  may  be  brought 
against  'interpretation  of  propositions'  is  that  it 
tends  to  confuse  two  different  things,  namely,  the 
import  or  meaning  of  propositions,  and  the  question 
of  what  other  statements  we  are  committed  to  in 
making  any  statement  whatever.  We  shall  speak 
of  the  'implications  of  propositions,'  since  the  ques- 
tions that  are  to  be  considered  in  this  chapter  relate 
to  the  various  methods  of  determining  the  relations 
that  exist  between  our  formally  expressed  proposi- 
tions, and  other  unexpressed  propositions  with 
which  they  are  immediately  connected.  Implication 
etymologically  means  'folded-in,'  so  that  the  idea 
the  topic  suggests  is  that  folded  within  any  state- 
ment we  make  there  are  other  statements  that  may 
be  brought  to  light  by  the  use  of  appropriate  meth- 
ods. The  practical  value  of  this  chapter  consists  in 
the  opportunity  it  affords  of  finding  out  that  our 
statements  ordinarily  mean  much  more  than  we 
actually  express  in  them. 

We  have  to  consider  two  main  classes  of  impli- 
cations : 

(1)  The  Opposition  of  Propositions.  By  op- 
position of  propositions  is  meant  the  relation  that 
the  truth  or  falsity  of  one  proposition  has  to  the 
truth  or  falsity  of  other  propositions  dealing  with 
the  same  subject-matter,  that  is,  having  the  same 
subject  and  predicate. 

(2)      Eductions.      By    eductions    is    meant    the 
relation  that  one  proposition  accepted  as  true  has 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   265 

to  other  propositions  dealing  with  the  same  subject- 
matter  from  other  points  of  view. 

The  Opposition  of  Propositions.  The  term  oppo- 
sition applied  to  propositions  would  strictly  mean 
that  propositions  could  stand  in  this  relation  only 
when  the  truth  of  the  one  involved  the  falsity  of 
the  other,  and  vice  versa.  This  was  the  original 
meaning  and  use  of  the  term  in  logic.  But  it  was 
found  convenient  to  include  under  the  same  title  a 
consideration  of  propositions  that  are  not  incompat- 
ible with  one  another.  Opposition,  as  it  is  now  used, 
embraces,  therefore,  a  study  of  the  relations  of  any 
two  propositions  referring  to  the  same  subject- 
matter  whether  the  truth  expressed  by  one  is  or  is 
not  compatible  with  that  expressed  by  the  other. 
Thus,  propositions  relating  to  the  same  subject,  but 
differing  in  quantity,  or  quality,  or  both,  are  said 
to  be  opposed  to  each  other. 

Since  there  are  only  four  categorical  proposi- 
tions, it  is  evident  that  each  stands  in  relation  to 
three  others.  Thus: 

SaP  is  related  to  SeP,  SiP,  SoP. 

SeP  is  related  to  SaP,  SiP,  SoP. 

SiP  is  related  to  SaP,  SeP,  SoP. 

SoP  is  related  to  SaP,  SeP,  SiP. 

If  we  examine  this  list  of  possible  oppositions, 
we  shall  see  that  each  proposition  is  related  to  (1) 
a  universal  proposition,  (2)  a  particular  proposi- 
tion, (3)  an  affirmative  proposition,  (4)  a  negative 
proposition.  In  other  words,  all  propositions  are 
related  to  others  (1)  of  the  same  and  (2)  different 


266  A  TEXT-BOOK   OF  LOGIC 

quantity,  and  (3)  of  the  same  and  (4)  different 
quality.  There  are,  consequently,  four  kinds  of 
opposition  in  which  any  proposition  may  stand. 
Thus,  the  relation  between 

1.  Universal  propositions  of  different  quality 
is  said  to  be  one  of  contrariety :    SaP,  SeP. 

2.  Universal  and  particular  propositions  of  the 
same  quality  is  said  to  be  one  of  subalternation : 
SaP,  SiP;  SeP,  SoP. 

3.  Universal  and  particular  propositions  of  dif- 
ferent quality  is  said  to  be  one  of  contradiction: 
SaP,  SoP;  SeP,  SiP. 

4.  Particular  propositions  is  said  to  be  one  of 
subcontrariety :    SiP,  SoP. 

We  shall  consider  each  of  these  kinds  of  opposi- 
tion in  the  order  in  which  they  have  been  named; 
and  since  any  statement  we  make  may  be  either  true 
or  false,  we  shall  have  to  examine  the  propositions 
that  stand  in  opposition  on  the  supposition  both  of 
their  truth  and  falsity. 

Contrariety.  Contrary  opposition  exists  between 
universal  propositions  of  a  different  quality;  that 
is,  between  SaP  and  SeP.  Thus,  contrary  proposi- 
tions differ  in  quality  only. 

If  what  any  universal  proposition  states  is  true, 
what  its  contrary  states  must  be  false.  For  example, 
if  it  is  true  that  'All  men  die/  it  is  false  that  'No 
men  die.'  If  it  is  true  that  'No  men  are  angels,'  it 
is  false  that  'All  men  are  angels.'  If,  therefore,  we 
accept  the  truth  of  what  either  SaP  or  SeP  states, 
the  falsity  of  what  its  contrary  states  follows  as  a 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS    267 

matter  of  course,  for  the  reason  that  the  same  pred- 
icates or  qualities  cannot  belong,  and  not  belong,  to 
the  same  subject.  On  the  other  hand,  if  what  any 
universal  proposition  states  is  false,  what  its  con- 
trary states  is  left  in  doubt.  If,  for  example,  it  is 
false  that  'All  men  are  six  feet  tall,'  we  are  left  in 
doubt  as  to  whether  'No  men  are  six  feet  tall,'  be- 
cause some  men  may  be. 

Let  us  connect  these  facts  with  what  we  have 
already  learned.  We  saw,  in  the  chapter  on  terms, 
that  if  two  species  of  a  genus  differ  from  one  an- 
other more  than  they  do  from  any  of  the  other  co- 
ordinate species,  the  relation  in  which  they  stand  is 
one  of  contrariety.  If,  for  example,  within  the  genus 
G  the  species  S  have  the  characteristic  P,  then  how- 
ever great  and  numerous  the  increasing  differences 
between  one  species  and  another,  they  cannot  be  so 
great  and  numerous  that,  within  the  genus,  P  can 
be  denied  of  any  of  the  species.  Based  upon  the 
degree  of  their  variation  from  the  genus,  all  the 
species,  as  we  have  seen,  have  a  recognised  place 
within  the  genus.  But  whatever  the  variations  that 
occur,  the  species  are  held  together  by  their  common 
likeness,  and  so  long  as  predication  is  concerned 
with  this  common  likeness,  so  long  can  we  not  en- 
tertain any  proposition  which  denies  it  of  any  or  of 
all  the  species  of  the  genus.  If  SaP  is  true,  the 
proposition  that  denies  that  S  is  P,  SeP,  must  be 
false,  and  vice  versa. 

Let  us  look  at  the  other  case  where  something 
is  falsely  predicated  of  all  the  species.  Now  what  is 


268  A  TEXT-BOOK   OF  LOGIC 

thus  predicated  cannot  be  the  genus,  for  the  genus 
can  only  be  predicated  truly.  If  anything  is  falsely 
predicated,  it  must  be  something  that  is  either  an- 
other genus,  when  the  statement  would  be  abso- 
lutely false,  or  something  that  is  or  may  be  a  differ- 
entia, when  the  statement  will  be  partially  false. 
If,  for  example,  'All  flesh  is  grass'  were  to  be  inter- 
preted literally,  the  statement  would  be  false,  be- 
cause it  predicates  a  genus  that  is  wholly  mislead- 
ing; and  if  one  were  to  say  that  'All  vertebrates 
live  in  the  water,'  that  would  be  false,  because  it 
predicates  what  is  or  may  be  a  differentia,  some- 
thing that  belongs  to  one  of  the  species  though  not 
to  all  of  them.  In  order  to  detect  the  falsity  in  these 
instances,  we  must  know  that  what  is  predicated  is 
either  a  wrong  genus  or  a  differentia,  and  this  is  not 
possible  without  going  beyond  what  is  given  in  a  false 
statement.  Hence,  if  all  we  know  is  that  P  is 
wrongly  predicated  of  S,  we  cannot  say  whether  P 
belongs  in  part  or  not  at  all  to  S,  and,  therefore,  can- 
not infer  the  truth  of  the  contrary  of  the  original 
proposition.  The  contrary  of  a  false  universal,  that 
is  to  say,  is  involved  in  doubt. 

Again,  the  relations  of  contrary  propositions 
may  be  studied  from  the  side  of  the  denotation 
of  their  terms.  Thus,  it  cannot  be  true  that  'All' 
and  'None'  of  the  objects  denoted  by  the  subject 
term  of  a  proposition  have  the  qualities  connoted 
by  the  predicate  term ;  the  truth  of  the  one  excludes 
the  truth  of  the  other.  That  the  falsity  of  one  prop- 
osition involves  its  contrary  in  doubt  may  be  shown 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   269 

as  follows:  If  some  of  the  objects  denoted  by  the 
predicate  term  of  an  affirmative  proposition,  and 
none  of  the  objects  denoted  by  the  same  term  in  a 
negative  proposition,  belong  to  the  group  of  objects 
denoted  alike  by  the  subject  terms  of  these  proposi- 
tions, then  it  is  obvious  that  in  the  one  case  P  falls 
partly  within,  and  in  the  other  wholly  without,  the 
group  of  objects  denoted  by  the  subject  terms  of 
the  two  propositions.  If,  now,  we  make  the  state- 
ment falsely  that  'All  S  falls  within  P  without  ex- 
hausting it/  we  connot  affirm  truly  the  contrary  of 
this  statement,  'No  S  falls  within  P/  because  there 
is  another  alternative  to  the  one  offered  by  the  con- 
trary, namely,  the  case  where  S  falls  partly  within 
and  partly  without  the  class  of  objects  denoted  by 
P;  and  which  of  these  two  cases  is  true  cannot  be 
determined  without  examining  the  cases  themselves. 
Representing  these  facts  diagrammatically  thus : 


we  must  say  that  if  SaP  is  false,  SeP  cannot  be 
true  without  disposing  of  the  alternative  case  SiP. 
But  this  cannot  be  done  formally,  but  only  by  an 
examination  of  the  subject-matter  of  these  propo- 
sitions. 

Subalternation.  Subaltern  opposition  exists  be- 
tween a  universal  and  a  particular  proposition  of 
the  same  quality;  that  is,  between  SaP  and  SiP; 


270  A   TEXT-BOOK   OF  LOGIC 

SeP  and  SoP.     Thus,  subaltern  propositions  differ 
in  quantity  only. 

If  what  the  universal  proposition  states  is  true, 
what  its  subaltern  states  is  also  true.  This  follows 
from  the  fact  that  universal  propositions  distribute 
their  subject  terms.  Thus,  if  something  is  true  or 
false,  as  the  universal  states,  of  each  of  a  class  of 
objects,  it  is  true  or  false  of  any  number  of  them, 
since  these  must  be  identical  with  some  of  the  for- 
mer. The  truth,  therefore,  of  the  particular  is  in- 
volved in  the  truth  of  the  universal  proposition. 
Hence,  as  may  be  seen  by  studying  the  accompany- 
ing diagram,  if  any  part  of  the  S  that  falls  wholly 


SaP  SiP  SeP  SoP 


within  P,  (SaP),  or  wholly  without  P,  (SeP),  were 
to  fall  partly  without  or  partly  within  P,  some  part 
of  S  would,  in  the  one  case,  fall  partly  within  (SiP) , 
and,  in  the  other,  partly  without  (SoP)  P,  and  it  is 
of  these  parts  that  the  statements  of  the  respective 
subaltern  propositions  is  made. 

On  the  other  hand,  if  what  the  universal  proposi- 
tion states  is  false,  what  its  subaltern  states  is  left 
in  doubt.  The  truth  of  the  particular  is  not  involved 
in  the  falsity  of  the  universal,  and  cannot,  there- 
fore, be  the  ground  of  the  latter's  falsity.  But,  as 
we  shall  see,  it  may  be.  We  have  studied  already 
one  ground  of  falsity  of  universal  statements.  We 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   271 

have  seen,  for  example,  that  when  the  contrary  of 
any  proposition  is  true,  that  proposition  is  abso- 
lutely false.  But  we  have  also  seen  that  if  we  start 
with  the  falsity  of  a  universal  statement,  nothing 
can  be  affirmed  as  to  the  truth  or  falsity  of  its  con- 
trary. Now,  in  contrast  to  the  falsity  involved  in 
the  contrary  relation,  that  involved  in  the  subaltern 
relation  is  only  relative,  that  is,  the  falsity  may  be 
due  not  to  the  fact  that  S-P  asserts  something  con- 
trary to  fact,  but  that  it  is  asserted  without  regard 
to  existing  limitations.  In  other  words,  since  there 
are  degrees  of  error,  as  well  as  of  truth,  SaP  and 
SeP  may  owe  their  falsity  to  the  fact  that  only  SiP 
and  SoP  are  true  respectively.  But,  here  again,  if 
we  start  with  the  falsity  of  the  universal,  we  cannot 
say  that  its  subaltern  is  true  or  false;  truth  or 
falsity,  in  this  case,  simply  remain  possible  alter- 
natives between  which  we  can  decide  only  by  going 
outside  wha't  is  given  in  the  original  proposition. 
And  this  is  equivalent  to  saying  that  the  subaltern 
is  always  involved  in  doubt  when  all  that  we  know 
is  that  the  universal  or  subalternans  is  false. 

What  we  have  seen  is  that  the  truth  of  a  univer- 
sal involves  the  truth  of  its  subaltern ;  but  that  the 
falsity  of  a  universal  involves  its  subaltern  in  doubt. 

Let  us  now  consider  how  the  universal  is  affected 
by  the  truth  or  falsity  of  its  particular,  subaltern, 
proposition.  And,  first,  let  us  take  the  case  where 
the  subaltern  is  true.  If  the  only  thing  we  know 
about  a  group  of  objects  is  that  some  of  them  are 
in  a  particular  place,  it  is  obvious  that  we  cannot 


272  A  TEXT-BOOK  OF  LOGIC 

say  that  they  are  all  in  that  place;  and  the  reason 
is  not  that  some  are  in  another  place,  for  that  ex- 
ceeds the  knowledge  contained  in  the  original  prop- 
osition, but  that  some  may  be.  For  a  similar  reason, 
we  cannot  affirm  that  'No  trees  are  in  leaf/  if  all 
that  we  know  is  that  'Some  trees  are-not  in  leaf/ 
From  the  truth  of  a  particular  proposition,  there- 
fore, we  can  only  conclude  that  its  subalternans — the 
universal  of  the  same  quality  —  is  doubtful.  Let 
us  take,  secondly,  the  case  where  the  subaltern  is 
false.  Here  the  falsity  of  the  subaltern  involves 
the  falsity  of  the  subalternans.  Thus,  if  'Some  apples 
are  blue'  is  false,  it  is  likewise  false  that  'All  apples 
are  blue/  and  if  'Some  apples  are-not  red'  is  false, 
it  is  likewise  false  that  'No  apples  are  red/  The 
reason  for  this  case  is  found  in  the  fact  that  par- 
ticular propositions  affirm  or  deny  a  predicate  of 
certain  unspecified  objects  of  a  class,  and  not  of  the 
class  as  a  whole.  If,  therefore,  we  know  that  a 
statement  is  false  in  some  case,  we  know  that  it 
cannot  be  true  of  all  cases,  since  all  cases  must  in- 
clude the  case  in  which  it  is  known  to  be  false. 
Falsus  in  uno,  falsus  in  omnibus.  We  are  dealing 
here  with  the  exception  under  which  a  rule  breaks 
down. 

Contradiction.  Contradictory  opposition  exists 
between  a  universal  and  a  particular  proposition 
that  differ  from  each  other  in  quality;  that  is,  be- 
tween SaP  and  SoP,  SeP  and  SiP.  Thus,  contradic- 
tory propositions  differ  both  in  quantity  and  quality. 

If  what  any  universal  proposition  states  is  true, 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   273 

what  its  contradictory  states  must  be  false.  If  it 
be  true  that  'All  men  are  willing  to  give  their  lives 
for  a  cause/  it  is  false  that  'Some  men  are-not  will- 
ing to  give  their  lives  for  a  cause.'  If  it  is  true  that 
'No  men  are  utterly  selfish/  it  is  false  that  'Some 
men  are  utterly  selfish/  If,  on  the  other  hand,  what 
a  universal  proposition  states  is  false,  what  the  con- 
tradictory opposite  states  must  be  true.  For  ex- 
ample, if  it  is  false  that  'Every  man  has  his  price/ 
it  is  true  that  'Some  men  cannot  be  bought/  and  if 
it  is  false  that  'None  of  the  candidates  were  suc- 
cessful/ it  is  true  that  some  were.  Further,  the 
truth  or  falsity  of  particular  propositions  involves 
the  falsity  or  truth  of  their  contradictories.  If 
'Some  one  is  going  to  get  hurt/  is  true,  it  is  false 
that  'No  one  is  going  to  get  hurt/  but  if  the  state- 
ment is  false,  then  'No  one  is  going  to  get  hurt*  is 
true.  If  'Some  people  are  short  sighted'  is  true,  it 
is  false  that  'No  people  are  short  sighted  /  but  if  it 
is  false  that  'Some  kinds  of  ignorance  promote  vir- 
tue/ it  is  true  that  'No  kinds  of  ignorance  promote 
virtue/ 

We  may  express  these  results  in  the  single  state- 
ment that  the  truth  of  one  of  the  propositions  in 
contradictory  opposition  involves  the  falsity  of  the 
other ;  and  the  falsity  of  one,  the  truth  of  the  other. 
Of  any  pair  of  contradictory  propositions,  one  must 
be  false,  and  the  other  true.  Contradiction  is,  there- 
fore, the  most  complete  form  of  logical  opposition. 

Subcontrariety.  Subcontrary  opposition  exists 
between  particular  propositions  of  different  quality ; 

18 


274  A  TEXT-BOOK   OF  LOGIC 

that  is,  between  SiP  and  SoP.     Thus,  subcontrary 
propositions  differ  in  quality  only. 

If  we  make  the  two  statements  that  'Some  men 
are  blue-eyed'  and  'Some  men  are-not  blue-eyed,' 
each  of  these  statements  is  true,  and  they  are  in 
subcontrary  relation  to  each  other.  But  the  truth 
of  either  one  of  them  is  not  sufficient  to  establish 
the  truth  of  the  other.  If,  for  example,  we  repre- 
sent our  two  propositions  thus : 


SiP  SoP 


it  will  be  evident  that  in  each  case  P,  in  part  or 
whole,  is  predicated  of  a  different  part  of  S. 
If,  consequently,  we  know  that  'Some  indeterminate 
number  of  men  are  blue-eyed,'  (SiP),  this  is  not  a 
sufficient  ground  for  saying  that  the  rest  are,  or  are 
not,  blue-eyed.  The  fact  that  we  are  dealing  with 
particular  propositions  which  have  undistributed 
subject  terms,  that  is,  terms  that  do  not  take  into 
account  a  determinate  number  of  instances  of  the 
class,  but  only  more  or  less  of  them,  prevents  us 
from  saying  anything  definite  of  the  rest  of  the  class 
with  respect  to  their  being  or  not  being  blue-eyed. 
Of  the  propositions,  therefore,  that  exist  in  subcon- 
trary opposition,  we  may  say  that  the  truth  of 
the  one  leaves  the  truth  of  the  other  in  doubt. 

Propositions  in  the  subcontrary  relation  cannot 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   275 

both  be  false.  In  other  words,  the  falsity  of  one  in- 
volves the  truth  of  the  other.  For  example,  if  it  is 
false  that  'Some  men  are  four-footed,'  it  is  true  that 
'Some  men  are-not  four-footed.'  That  is,  it  is  only 
on  condition  that  some  men  are  not  four-footed  that 
we  can  deny  the  truth  of  the  statement  that  'Some 
men  are  four-footed.'  This  view  of  subcontrary 
opposition  is  required  by  the  fact  that  if  both  par- 
ticular propositions  were  false,  their  contradictories 
would  both  be  true;  but,  as  we  have  seen,  SaP  and 
SeP  cannot  both  be  true,  for  if  one  is  true  the  other 
is  proved  to  be  false.  But  if,  as  we  have  seen,  the 
falsity  of  the  universal  —  'All  men  are  four-footed/ 
for  example  —  involves  its  contrary  in  doubt,  we 
can  at  least  say  that  its  contradictory  —  'Some  men 
are-not  four-footed'  —  is  true. 

The  Square  of  Opposition.  The  accompanying 
diagram,  called  the  Square  of  Opposition,  is  a  me- 
chanical devise  which  has  long  been  traditional  in 
logic,  and  is  intended  as  an  aid  to  the  better  under- 
standing of  the  doctrine  of  opposition.  The  univer- 
sal propositions  are  placed  at  the  top,  the  particular 
propositions  at  the  bottom  of  the  diagram;  the 
affirmative  propositions  are  placed  on  the  left,  and 
the  negative  ones  on  the  right.  The  lines  connecting 
any  two  propositions  indicate  the  kind  of  opposition 
that  exists  between  them.  The  top  and  bottom  lines 
which  are  horizontal  and  parallel  to  each  other  con- 
nect propositions  of  the  same  quantity ;  the  side  lines 
which  are  perpendicular  and  parallel  connect  prop- 
ositions of  the  same  quality.  The  long  diagonal  lines 


276 


A  TEXT-BOOK   OF  LOGIC 


connect  propositions  that  are  different  in  both  quan- 
tity and  quality. 


Let  us  now  see  how  it  may  be  used  to  throw 
light  on  the  doctrine  of  opposition.  It  will  be  ob- 
served at  once  that  every  proposition  has  its  con- 
tradictory, and  in  contradiction,  it  will  be  remem- 
bered, we  have  the  most  complete  form  of  logical 
opposition.  To  work  the  relations  of  opposition  out 
under  the  control  of  the  contradictory  relation  seems 
to  simplify  the  whole  matter  for  most  students.  We 
summarise  the  doctrine  of  opposition  below,  and  the 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS    277 

student  is  required  to  follow  the  statements  out  on 
the  Square  of  Opposition.    Thus,  if 

SaP  is  true,  its  contradictory  and  its  contrary 
are  false,  and  its  subaltern  is  true. 

SaP  is  false,  its  contradictory  is  true,  and  its 
contrary  and  its  subaltern  are  doubtful. 

SeP  is  true,  its  contradictory  and  its  contrary 
are  false,  and  its  subaltern  is  true. 

SeP  is  false,  its  contradictory  is  true,  and  its 
contrary  and  its  subaltern  are  doubtful. 

SiP  is  true,  its  contradictory  is  false,  and  its 
subcontrary  and  subalternans  are  doubtful. 

SiP  is  false,  its  contradictory  and  sub-contrary 
are  true,  and  its  subalternans  is  false. 

SoP  is  true,  its  contradictory  is  false,  and  its 
subcontrary  and  subalternans  are  doubtful. 

SoP  is  false,  its  contradictory  and  sub-contrary 
are  true,  and  its  subalternans  is  false. 

It  may  be  helpful  to  represent  these  facts  and 
relations  diagrammatically.  This  we  may  do  by 
drawing  only  so  much  of  the  Square  of  Opposition 
as  embodies  the  relations  in  which  a  given  proposi- 
tion stands,  utilising  the  arrow  head  to  indicate  the 
direction  in  which  given  relations  are  to  be  read. 
For  example,  the  lines  _^J  diverge  from  a  common 
point  and  indicate,  according  to  their  direction,  the 
propositions  we  are  considering  and  the  relations  in 
which  they  stand.  It  is  obvious  that  the  example 
chosen  is  the  0  proposition.  Since,  then,  the  direc- 
tion of  the  lines  tells  us  what  propositions  we  are 


278 


A  TEXT-BOOK   OF  LOGIC 


dealing  with,  and  in  what  relations  of  opposition 
they  stand,  we  may  indicate  at  the  ends  of  the  lines 
whether,  in  those  relations,  the  proposition  is  true 
(T) ,  false  (F) ,  or  doubtful  (D) .  Further,  we  may 
indicate  the  original  proposition  by  writing  its  given 
truth  or  falsity  in  a  circle.  Following  these  direc- 
tions, we  have  the  accompanying  result : 


A  summary  of  the  doctrine  of  opposition  is  given 
in  the  table  on  page  279. 

Nature  and  Methods  of  Eduction.  In  the  course 
of  our  study,  we  have  seen  that  all  our  judgments 
are  related  to  other  judgments  referring  to  the  same 
subject-matter,  and,  consequently,  that  every  judg- 
ment implies  more  than  it  asserts.  Put  more 
directly,  every  judgment  commits  us  not  only  to 
what  we  assert,  but  also  to  the  acceptance  of  all 
the  other  judgments  which  are  implied  in  what  we 
assert.  Now  when  these  implied  judgments  involve 
a  change  in  the  point  of  view  from  which  the  sub- 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   279 

ject-matter  of  the  original  judgment  is  viewed,  they 
are  called  eductions. 

We  may  classify  the  methods  of  eduction  as  ob- 
version,  conversion,  contraposition,  and  inversion. 
But  only  two  of  these  methods,  obversion  and  con- 
version, are  fundamental.  In  the  following  sections, 
we  shall  study  the  fundamental  methods  first,  and 
follow  this  with  a  consideration  of  the  derived 
methods,  contraposition  and  inversion. 


Given 

SaP 

SeP 

SiP 

SoP 

F 

T 

F 

""I       F 

D 

D 

T 

ScP    ? 

F 

F 

T 

f      F 

D 

T 

D 

D 

F 

D 

{      F 

F 

T 

T 

RnP       ) 

F 

D 

D 

I            F 

T 

F 

T 

TABLE  OF  OPPOSITIONS 

Obversion.  Other  terms  by  which  this  method 
is  sometimes  known  are  Permutation,  Aequipollence, 
Immediate  inference  by  Private  Conception.  Obver- 
sion is  the  logical  form  of  the  double  negative  with 
which  we  have  all  become  acquainted  in  the  study 


280  A  TEXT-BOOK   OF  LOGIC 

of  grammar.  Like  the  double  negative,  it  has  the 
force  of  changing  an  affirmative  statement  into  a 
negative  one,  and  a  negative  statement  into  an 
affirmative  one.  Obversion_effects  no  change  in  the 
meaning  of  what  is  assertednbuT~onTy  in  its  em- 
phasis. For  example,  'Barkis  jgL.willin* '  by  obver- 
sion  becomes  'Barkis  is-not  unwillin';'  'To  do  this 
is-not  unnecessary'  becomes  by  obversion  To  do  this 
is  necessary.' 

In  obversion  only  the  quality  of  the  original 
proposition,  called  the  obvertend,  undergoes  change ; 
the  quantity  and  the  meaning  remain  the  same.  But 
if  the  quality  changes,  the  predicate  term  of  the 
obvertend  must  also  undergo  modification  if  the 
meaning  is  to  remain  unaffected.  What  exactly  is 
this  modification?  It  cannot  be  enough  to  say  that 
the  characteristic  of  the  obverse  of  a  proposition  is 
that  it  has  for  its  predicate  term  the  negative  of 
the  predicate  of  the  proposition  from  which  it  is  de- 
rived, although,  of  course,  this  is,  from  the  formal 
point  of  view,  true.  Nor  can  we  say  that  the  con- 
notation of  the  obvertend  is  affected,  for  that  is  the 
question  we  are  raising.  If  we  are  to  understand 
the  particular  significance  of  obversion,  we  shall 
have  to  interpret  it  as  a  method  that  affects  the 
meaning  of  a  proposition  by  a  change  in  what  the 
proposition  denotes.  That  is  to  say,  the  particular 
range  of  the  objects  signified  by  the  obvertend  is 
different  from  that  of  its  obverse.  For  example,  in 
the  illustrations  used  above,  it  is  obvious  that 
Barkis'  attitude  must  be  one  of  willingness  or  un- 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   281 

willingness;  and  of  any  action  we  may  say  that  it 
is  necessary  or  unnecessary.  Now,  since  obversion 
is,  in  part,  a  matter  of  negation,  we  carry  over  into 
that  process  all  the  characteristics  that  make  nega- 
tion significant.  We  have  seen  that  negation  is  very 
largely  a  matter  of  the  emphasis  that  we  give  to 
our  knowledge,  and  of  the  definiteness  or  indefinite- 
ness  of  our  acquaintance  with  what  we  assert. 
Thus,  if  we  are  not  sure  of  the  degree  of  Barkis' 
willingness,  we  may  express  the  actual  state  of  our 
information  or  opinion  by  saying  that  he  is  not- 
unwilling.  If  we  wish  to  suggest,  but  not  to  state 
explicitly,  the  degree  of  necessity  of  the  things  we 
do,  we  may  say  that  they  are  not-unnecessary.  A 
guarded  statement  of  the  latter  kind,  it  will  be  ob- 
served, becomes  more  emphatic  by  obversion,  for 
we  are  thereby  led  to  assert  without  qualification  the 
necessity  of  our  actions. 

There  are  two  steps  in  the  process  of  obversion ; 
the  first  consists  in  changing  the  quality  of  the 
original  proposition  without  changing  its  quantity; 
the  second  consists  in  negating  the  predicate  term 
of  the  original  proposition.  To  consider  the  first 
step  we  should  observe,  with  respect  to  quantity, 
that  if  the  original  proposition  is  universal  the  de- 
rived proposition  is  universal,  and  if  the  original 
proposition  is  particular  the  derived  proposition  is 
particular;  and,  with  respect  to  quality,  that  if  the 
original  proposition  is  affirmative  the  derived  prop- 
osition is  negative,  and  that  if  the  original  proposi- 
tion is  negative  the  derived  proposition  is  affirm- 


282 


A   TEXT-BOOK   OF  LOGIC 


ative.  Combining  these  two  considerations,  we  find 
that,  in  obversion,  an  A  proposition  always  changes 
to  an  E,  an  E  to  an  A,  an  I  to  an  O,  and  an  0  to  an 
I.  With  regard  to  negating  the  predicate  term  of 
the  original  proposition,  the  second  step  in  obver- 
sion, we  may  observe  that  if  we  use  a  short  horizon- 
tal stroke  over  the  symbol  of  an  affirmative  predicate 
term  to  indicate  that  that  term  has  been  negated, 
it  will  be  obvious  that  obverted  propositions  are 
characterised  generally  by  having  for  their  predicate 
terms  the  so-called  infinite  or  non-P  term.  It  fol- 
lows that  if  the  predicate  term  is  already  a  negative 
or  infinite  term,  the  effect  of  negating  it  will  be  to 
remove  the  sign  of  negation.  The  method  of  indi- 
cating negation  by  the  short  horizontal  stroke  over 
the  symbol  of  an  affirmative  term  is  used  throughout 
this  book,  and  this  fact  should  be  noted;  a  horizon- 
tal stroke  over  any  term,  whether  predicate  or  sub- 
ject term,  will  have  the  meaning  of  negation.  Thus, 
U  will  mean  non-S,  M  will  mean  non-M,  just  as  P* 
means  non-P.  With  these  explanations  the  method 
of  obversion  should  be  sufficiently  clear.  In  the  fol- 
lowing table  we  illustrate  the  method  of  obversion  in 
each  of  the  four  categorical  propositions : 


Obvertend 

SaP 

SeP 

SiP 

SoP 

First  Step 

Second  Step 
Obverse 

SeP 

SaP 

SoP 

SiP 

SeP 

SaP 

SoP 

SiP 

TABLE  OF  OBVERSIONS 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   283 

Conversion.  This  is  a  process  by  which  we  affirm 
or  deny  of  the  predicate  term  of  an  original  prop- 
osition, called  in  this  relation  the  con vertend,  what 
was  asserted  by  the  subject  term  of  the  same  prop- 
osition. If,  for  example,  we  know  that  'JMlocarpin 
when  taken  internally  is  followed  by  a  slowing  of 
the  heart  beat,'  we  are  able,  by  conversion,  to  place 
pilocarpin  among  the  agents  which  have  the  effect 
of  slowing  the  heart  beat  in  any  investigation  we 
may  make  about  the  conditions  under  which  the 
heart  beat  is  slowed.  In  other  words,  the  terms  by 
which  in  one  proposition  we  qualify  a  subject,  may 
themselves  become  of  direct  interest  to  us,  and  in 
looking  about  for  predicates  which  shall  qualify 
them,  we  find  in  the  original' proposition  something 
that  is  serviceable  for  this  purpose.  To  state  gen- 
erally the  fact  that  conversion  denotes,  we  may  say 
that  if  we  make  any  statement  in  the  S-P  form, 
conversion  is  the  answer  to  the  question  whether  we 
are  able,  because  we  have  made  this  statement,  to 
make  another  which  will  have  the  form  P-S.  Hav- 
ing said  something  about  S,  can  we,  therefore,  say 
something  about  P? 

That  this  is  a  very  reasonable  inquiry  will  ap- 
pear if  we  recall  what  was  said  about  the  possibility 
of  predicating  of  any  term  S  another  P.  We  saw 
that  this  possibility  rests  upon  the  fact  that  S  is  not 
merely  S,  and  that  P  is  not  merely  P.  In  any  judg- 
ment we  are  dealing  with  a  complex  phenomenon, 
and  our  statements  reflect  this  fact.  We,  therefore, 
said  that  the  S  that  in  any  proposition  is  P  is  an 


284  A  TEXT-BOOK   OF  LOGIC 

SP,  and,  as  we  also  saw,  the  P  that  is  predicated 
of  S  has  its  roots  running  down  into,  and  derives 
its  character  from,  the  same  ground  that  makes  of 
S  a  significant  term.  In  other  words,  the  P  of  any 
proposition  is  also  an  SP.  It  is  this  fact  that  under- 
lies the  process  and  problem  of  conversion.  If  S  is 
P  at  all,  then  the  conditions  of  its  being  P  are  those 
that  will  enable  us  to  reverse  the  relation,  and  to 
declare  that  P  is  S.  This  is  the  general  statement 
of  the  fact  of  conversion,  but  what  the  limitations 
are  under  which  conversion  may  legitimately  take 
place  must  be  ascertained  from  the  study  of  con- 
crete cases.  In  other  words,  conversion  is  not  a 
wholly  formal  process,  it  is  not  a  mere  manipulation 
of  symbols;  but  a  study  of  the  formal  relations  of 
the  terms  of  the  proposition  brings  to  light  some 
of  the  limits  of  this  type  of  thinking. 

Formally  considered,  conversion  is  the  method 
by  which  the  predicate  term  of  one  proposition, 
called  the  convertend,  becomes  the  subject  term  of 
another,  called  the  converse,  and  the  subject  term 
of  the  former  proposition  becomes  the  predicate 
term  of  the  latter.  It  will  be  seen,  then,  that  the 
terms  of  the  converse  must  be  the  same  as  the  terms 
of  the  convertend.  Stated  simply,  the  terms  of  the 
converse  are  derived  from  the  convertend  by  the 
transposition  of  its  terms :  S-P  becomes  P-S.  Again, 
we  should  observe  that  in  conversion  there  is  no 
change  in  the  quality  of  the  proposition :  an  affirm- 
ative proposition  remains  affirmative,  and  a  neg- 
ative proposition  remains  negative.  And,  further, 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   285 

the  quantity  of  propositions  sometimes  is,  and  some- 
times is  not  affected  by  their  conversion.  This  will 
be  shown  in  our  examination  of  the  four  categor- 
ical propositions,  and  the  reason  for  it  will  then  be- 
come clear.  But  before  we  examine  each  kind  of 
proposition  to  ascertain  whether  and  in  what  form 
it  is  capable  of  conversion,  we  wish  to  call  attention 
to  the  rule  which  governs  all  cases  of  conversion, 
namely:  If  a  term  is  distributed  in  the  converse 
it  must  have  been  distributed  in  the  convertend. 
Practical  direction  for  applying  this  rule  may  be 
laid  down  thus :  Quantify  the  predicate,  and  trans- 
pose terms. 

The  simplest  cases  of  conversion  are  met  with 
in  the  universal  negative  and  the  particular  affirm- 
ative propositions:  SeP  and  SiP.  The  universal 
negative  proposition  has  two  distributed  terms,  and 
the  particular  affirmative  proposition  has  two  un- 
distributed terms.  It  follows  from  these  facts  that 
if  we  transpose  the  terms  of  each  proposition,  with- 
out changing  the  quality,  no  term  in  the  converse 
is  distributed  that  was  not  distributed  in  the  con- 
vertend. If,  for  example,  the  whole  of  P,  in  the 
universal  negative  proposition,  lies  outside  the  whole 
of  S,  then  the  whole  of  S  falls  outside  the  whole  of 
P.  In  the  case  of  the  particular  affirmative  prop- 
osition, some  of  S  is  identical  with  some  of  P,  and, 
therefore,  it  follows  that  the  same  part  of  P  is 
identical  with  the  same  part  of  S.  Under  these 
conditions,  it  is  possible  not  only  to  say  that  'S  is 
P,'  but  also  that  T  is  S.'  When,  as  in  these  two 


286  A  TEXT-BOOK   OF  LOGIC 

cases,  we  convert  a  proposition  without  changing 
its  quantity,  we  are  said  to  convert  simply,  or,  as 
the  Latin  word  has  it,  simpliciter. 

Conversion  by  limitation,  or  per  accidens,  that 
is,  conversion  that  involves  a  change  in  the  quantity 
of  a  proposition,  is  necessary  in  the  case  of  the  uni- 
versal affirmative  proposition,  SaP.  The  reason  for 
this  is  that,  being  an  affirmative  statement,  the 
predicate  term  is  undistributed,  and  when  this  be- 
comes the  subject  term  of  a  new  proposition,  it  does 
not  present  a  determinate  number  of  objects  for  the 
predicate  to  qualify.  For  example,  'All  the  books 
are  on  that  shelf  cannot  imply  that  'All  the  things 
on  that  shelf  are  books ;'  there  may  be  other  things 
on  the  shelf  than  books.  All,  therefore,  that  we  are 
warranted  in  saying  is  that  'Some  of  the  things  on 
that  shelf  are  books,'  a  statement  that  differs  in 
quantity  from  the  original  proposition.  The  stu- 
dent may  find  examples  of  universal  affirmative 
propositions  which,  on  account  of  the  nature  of 
their  subject-matter,  admit  of  simple  conversion; 
but  the  form  of  the  proposition  does  not  show  this. 
'A  straight  line  is  the  shortest  distance  between  two 
points/  that  is  to  say,  definitions,  may  serve  to  show 
what  is  meant.  So  long,  however,  as  we  confine 
attention  to  the  form  of  the  proposition,  SaP  con- 
verts by  limitation  to  PiS. 

A  particular  negative  proposition  cannot  be  con- 
verted at  all.  In  such  a  proposition  the  subject 
term  is  undistributed,  and  the  predicate  term  is  dis- 
tributed. If,  therefore,  we  transpose  the  terms,  we 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS  287 

have  a  proposition  with  a  distributed  subject  and 
an  undistributed  predicate,  that  is  a  proposition  of 
the  form  'All  S — some  P.'  Now  the  only  proposi- 
tion that  we  have  of  this  form  is  the  universal 
affirmative,  and  we  should  be  required  to  take  this 
as  such  a  proposition.  But  this  we  cannot  do,  be- 
cause the  converse  of  a  proposition  must  be  of  the 
same  quality  as  the  convertend,  and,  moreover,  no 
negative  proposition  has  an  undistributed  predicate 
term.  But  if,  in  order  to  overcome  this  difficulty, 
we  were  to  distribute  this  term,  we  infringe  the 
rule  of  conversion  which  states  that  if  a  term  is 
distributed  in  the  converse  it  must  have  been  dis- 
tributed in  the  convertend.  In  no  way,  therefore, 
can  we  convert  a  particular  negative  proposition. 
It  may  sometimes  be  true  that  SoP  and  PoS  are 
both  true,  but  we  must  go  outside  the  formal  rela- 
tions of  S  and  P  in  the  propositions  to  see  this.  For 
example,  'Some  anarchists  are-not  Italians/  and 
'Some  Italians  are-not  anarchists'  are  both  true. 
But  we  do  not  always  get  a  like  satisfactory  result 
merely  by  transposing  the  terms  of  particular  nega- 
tive statements.  For  example,  'Some  men  are-not 
professors'  is  true,  but  'Some  professors  are-not 
men'  is  false,  so  long,  that  is,  as  we  only  mean  by 
men  membership  in  the  human  race.  These  cases 
depend  upon  a  knowledge  of  more  than  the  original 
proposition  states,  and  there  is  no  possibility  of 
ascertaining  the  precise  nature  of  that  knowledge 
from  a  study  of  the  formal  relations  of  S  and  P  in 
a  particular  negative  proposition. 


288  A   TEXT-BOOK   OF   LOGIC 

We  add  below  a  table  of  all  possible  conversions : 


Convertend 

SaP 

SeP 

SiP 

SoP 

Converse 

PiS 

PeS 

PiS 

TABLE  OF  CONVERSIONS 

Contraposition.  Sometimes  called  Conversion  by 
Negation,  and  Contrapositive  Conversion.  The  con- 
trapositive  of  a  given  proposition  may  be  described, 
according  to  the  method  by  which  we  arrive  at  it, 
as  the  converted  obverse.  The  rule,  consequently, 
that  we  should  follow  to  reach  the  contrapositive 
of  any  proposition  is:  First  obvert  the  original 
proposition,  and  then  convert  the  proposition  thus 
obtained.  If  we  follow  this  rule,  the  contrapositive 
will  be  seen  to  be  a  proposition  that  has  for  its 
subject  term  the  negative  of  the  predicate  of  the 
original  proposition,  called  in  this  case  the  obver- 
tend.  S-P  becomes  P-S-  Now,  since  obversion  is 
involved  in  the  process  of  reaching  a  contrapositive, 
and  conversion  does  not  change  it  back  again,  the 
contrapositive  differs  in  quality  from  the  original 
proposition.  And  since  the  quantity  of  a  proposi- 
tion, as  we  have  seen,  is  sometimes  affected  by  con- 
version, namely,  when  the  proposition  is  a  univer- 
sal affirmative  proposition,  the  quantity  of  the  con- 
trapositive will,  in  that  case,  be  changed,  but  in  all 
other  cases  it  will  be  unaffected. 

The  contrapositive  of  any  proposition  may  be 
obverted,  and  the  proposition  thus  obtained  will 
have  the  characteristics  that  we  have  enumerated 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   289 


in  the  section  on  obversion.  Such  a  proposition  is 
called  the  obverted  contrapositive.  In  this  case 
P^-S,  the  contrapositive  of  S-P,  becomes  by  obver- 
sion P-& 

The  results  of  the  above  statements,  expressed 
symbolically,  are  given  in  the  following  table  of 
contrapositives  : 


Original  Proposition 

SaP 

SeP 

SiP 

SoP 

Obverse 

SeP 

SaP 

SoP 

SiP 

Contrapositive 

PeS 

PiS 

PiS 

Obverted  Contra 
positive 

PaS 

PoS 

PoS 

TABLE  OF  CONTRAPOSITION 

Not  many  examples  of  contraposition  are  neces- 
sary if  the  student  has  mastered  the  fundamental 
processes  of  obversion  and  conversion.  We  confine 
ourselves  to  one: 


Original 
Proposition 

SaP 

All  acids  are  substances  that  turn 
blue  litmus  paper  red 

Obverse 

SeP 

No  acids  are  substances  that  do 
not  turn  blue  litmus  paper  red 

Contrapositive 

PeS 

No  substances  that  do  not  turn 
blue  litmus  paper  red  are  acids 

Obverted 
Contrapositive 

PaS 

All  substances  that  do  not  turn 
blue  litmus  paper  red  are  non-acid 

19 


EXAMPLE  OF  CONTRAPOSITION 


290  A  TEXT-BOOK   OF  LOGIC 

Inversion.     The  inverse  of  a  proposition  has  for 
its  subject  the  contradictory  of  the  subject  of  the 

original  proposition  (invertend).  S-P  becomes  "S-P. 
Like  contraposition,  inversion  is  arrived  at  indi- 
rectly through  the  use  of  the  two  fundamental 
forms  of  eduction.  And  since  we  can  obtain  by 
obversion  the  contradictory  of  a  term  only  when 
that  term  forms  the  predicate  of  a  proposition,  S 
must  be  made  the  predicate  of  a  proposition  before 
its  contradictory  can  be  ascertained,  that  is,  con- 
version must  have  taken  place  at  some  stage  in  the 
process  of  inversion.  In  other  words,  S  must  have 
been  made  the  predicate  of  a  proposition,  and  then 
that  proposition  must  have  been  obverted  if  we  are 
to  get  a  non-S  term.  Inversion  can  apply  only  to 
the  two  universal  propositions,  SaP  and  SeP,  and  in 
each  case  we  get  a  particular  proposition  of  the  gen- 
eral form  ST-P.  We  must  follow  a  separate  rule  in 
each  of  these  cases.  To  invert  a  universal  affirmative 
proposition,  the  rule  reads:  Obvert  and  convert 
alternately  until  a  proposition  of  the  required  form 
is  found.  The  rule  for  the  universal  negative  prop- 
osition reads :  Convert  and  obvert  alternately  until 
a  proposition  of  the  required  form  is  found.  We 
show  the  necessary  steps  in  each  of  these  cases  in 
the  following  table : 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS   291 


Original 
Proposition 

SaP 

Obverse 

SeP 

Converse 

PeS 

Obverse 

PaS 

Converse 

SiP 

Inverse 

SoP 

Original 
Proposition 

SeP 

Converse 

PeS 

Obverse 

PaS 

Inverse 

SiP 

TABLES    OF   INVERSION 

,  We  may  obvert  these  inverses,  and  thus  obtain 
the  obverted  inverses.  Thus,  SoP  will  give  SiP,  and 
£5iP  will  give  ~SoP.  It  will  be  "observed  that  from 
the  universal  affirmative  proposition  we  get,  by  in- 
version, a  particular  negative  proposition,  and  from 
the  universal  negative  proposition  a  particular 
affirmative  proposition,  and  that  by  obversion  these 
inverses  are  given  the  same  quality  as  their  re- 
spective original  propositions. 

Summary  of  Eduction.  In  this  section  we  give 
first  an  outline  schema  of  the  characteristics  of  the 
propositions  arrived  at  by  eduction,  that  is,  we  show 
the  character  and  relations  of  the  terms  of  all  the 
eductive  propositions.  Thus: 


292 


A  TEXT-BOOK   OF  LOGIC 


Original  Proposition 

S-P 

Obverse 

S-P 

Converse 

P-S 

Contrapositive 

P-S 

Obverted  Contra 
positive 

P-S 

Inverse 

S-P 

Obverted  Inverse 

S-P 

SCHEMA  OF  EDUCTIVE  PROPOSITIONS 
In  the  following  table  we  show,  secondly,  all  the 
eductions  of  each  of  the  four  categorical  proposi- 
tions  in  a   form   which   indicates  throughout  the 
quantity  and  quality  of  the  propositions : 


Original  Proposition 

SaP 

SeP 

SiP 

SoP 

Obverse 

SeP 

SaP 

SoP 

SiP 

Converse 

PiS 

PeS 

PiS 

Obverted  Converse 

PoS 

PaS 

PoS 

Contrapositive 

PeS 

PiS 

PiS 

Obverted  Contra 
positive 

PaS 

PoS 

PoS 

Inverse 

SoP 

SiP 

Obverted  Inverse 

SiP 

SoP 

TABLE  OF  EDUCTIONS 


IMPLICATIONS  OF  CATEGORICAL  PROPOSITIONS  293 


REFERENCES 

H.  A.  Aikins,  The  Principles  of  Logic,  Chs.  IX.,  XI. 

J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Ch.  VII. 

J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Part  I.,  Chs. 
XII.,  XIII.,  XIV. 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Lessons  IX.,  X. 

J.  N.  Keynes,  Formal  Logic,  2d  Edition,  Part  II.,  Chs.  II., 
III.,  IV.,  V. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  III.,  Parts  ii.,  iii. 

W.  Minto,  Logic,  Inductive  and  Deductive,  Part  III.,  Ghs.  II., 
III. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Chs.  VI., 
VII. 

W.  J.  Taylor,  Elementary  Logic,  Ch.  VIII. 

ADVANCED 

B.  Bosanquet,  Logic,  Ch.  VII. 

W.  R.  B.  Gibson,  The  Problem  of  Logic,  Chs.  XIX,  XX. 
H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Chs.  IX.,  X. 
H.  Lotze,  Logic,  Vol.  I.,  Ch.  II.,  §§  75  to  82. 
F.  C.  S.  Schiller,  Formal  Logic,  Chs.  XII.,  XIII. 
J.  Welton,  A  Manual  of  Logic,  Vol.  I.,  Book  III.,  Chs.  II., 
III.,  §§  102,  103. 

QUESTIONS. 

1.  Classify   categorical   propositions    from   the   standpoint 
(1)  of  their  quantity  and   (2)   quality. 

2.  What  are  the  quantitative  and  qualitative  characteris- 
tics of  logical  statements. 

3.  What  symbols  are  used  to  distinguish  the  four  categor- 
ical propositions,  how  are  they  derived,  and  what  exactly 
do  they  represent? 

4  Explain  what  is  meant  by  a  structural  formula..  What 
is  the  general  structural  formula  of  a  categorical  prop- 
osition? 


294  A  TEXT-BOOK  OF  LOGIC 

6.     Write  the  structural  formulae  of  all  the  categorical  prop- 
ositions, and  explain  how  they  are  derived. 

6.  What  do  you  understand  by  the  distribution  of  terms? 

7.  What  determines  the  distribution  of  the  subject  terms 
of  propositions? 

8.  From  what  standpoint  is  the  distribution  of  the  pred- 
icate terms  of  propositions  determined? 

9.  What  is  the  distribution  of  each  of  the  terms  in  each 
of  the  four  categorical  propositions? 

10.  Explain  why  the  predicate  terms  of  affirmative  propo- 
sitions are  undistributed. 

XI.  Explain  why  the  predicate  terms  in  SeP  and  SoP  are 
distributed. 

12.  Classify  in  any  suitable  way  the  distribution  of  all  the 
terms  of  all  the  categorical  propositions. 

13.  What  is  meant  by  the  implication  of  propositions? 

14.  What  other  terms  have  been  used  to  describe  the  fact 
of  implication,  and  why  are  these  not  suitable? 

15.  What  are  the  main  classes  of  implication? 

16.  What  do  you  understand  by  the  Opposition  of  Proposi- 
tions? 

17.  Name    all    the    relations    of    opposition    of    categorical 
propositions. 

18.  Between   what   propositions    can    the   relation    of   con- 
trariety exist? 

19.  How  do  contrary  propositions  differ  from,  and  in  what 
respects  do  they  argee  with,  each  other? 

20.  If  one  of  the  propositions  existing  in  a  contrary  rela- 
tion is  true,  what  can  you  say  of  the  other? 

21.  Explain  why  a  proposition  is  doubtful  if  its  contrary 
is  false. 

22.  Between  what  propositions  can  the  subaltern  relation 
exist? 

23.  How  do  subaltern  propositions  differ  from,  and  in  what 
respects  do  they  argee  with,  each  other? 

24.  Why  does  the  truth  of  the  subalternans  involve  the  truth 
of  the  subaltern? 


IMPLICATIONS  OP  CATEGORICAL  PROPOSITIONS   295 

25.  Explain  why  a  proposition  is  doubtful  if  its  subaltern 
is  true. 

26.  Why  is  a  proposition  false  if  its  subaltern  is  false? 

27.  Between  what  propositions  can  the  contradictory  rela- 
tion exist? 

28.  How  do  contradictory  propositions  differ  from,  and  in 
what  respects  do  they  argee  with,  each  other? 

29.  Explain  why  the  truth  or  falsity  of  a  proposition  in- 
volves the  falsity  or  truth  of  its  contradictory. 

30.  Between  what  propositions  can  the  subcontrary  relation 
exist? 

31.  How  do   subcontrary  propositions   differ   from,   and   in 
what  respects  do  they  argee  with,  each  other? 

32.  Why  is  a  proposition  doubtful  if  its  subcontrary  is  true? 

33.  Explain  why  a  proposition  is  true  if  its  subcontrary  is 
false. 

34.  What  is  the  Square  of  Opposition? 

35.  What  are  Eductions? 

36.  Classify  the  Eductions. 

37.  Explain  and  illustrate  the  method  of  obversion. 

38.  Upon    what    characteristics    of    propositions    does    the 
method  of  conversion  rest? 

39.  Explain  and  illustrate  the  method  of  conversion. 

40.  What  is  the  rule  of  conversion? 

41.  Name  and  illustrate  the  classes  of  conversion. 

42.  Why  cannot  SoP  be  converted? 

43.  Are    there    any    particular    negative    propositions    that 
can  be  converted?    Illustrate. 

44.  If  your  answer  to  the  previous  question  is  in  the  affirm- 
ative, explain  why  logic  says  that  SoP  cannot  be  con- 
verted. 

45.  What  is  contraposition? 

46.  What  steps  must  be  taken  to  securj  the  contrapositive 
of  a  proposition? 

47.  Why  is  the  contrapositive  of  a  proposition   sometimes 
called  the  converted  obverse? 

48.  What  is  inversion? 


296  A  TEXT-BOOK   OF  LOGIC 

49.  What  is  the  method  of  finding  the  inverse  of  SaP? 

50.  How  do  you  proceed  to  find  the  inverse  of  a  universal 
negative  proposition? 

EXERCISES 

NOTE  —  State  propositions  in  logical  form  when  answer- 
ing a  question,  and  write  the  formula  for  each  proposition 
involved  in  your  answers. 

1.  Write  all  the  relations  of  Opposition  of: 

(1)  We  are  not  all  college  professors. 

(2)  Few  books  in  logic  are  easy  reading. 

(3)  The  old  paths  are  best. 

(4)  Improbable  events  happen  almost  every  day. 

(5)  The  longest  road  comes  to  an  end. 

(6)  Unasked  advice  is  seldom  acceptable. 

(7)  Only  ignorant  persons  hold  such  opinions. 

(8)  Infallibility  is  a  myth. 

2.  Give  the  converse  of: 

(1)  Mercy  but  murders,  pardoning    (  =  if  it  pardons) 
those  that  kill. 

(2)  We  cannot  all  command  success. 

3.  Give  the  obverse  of: 

(1)  Not  every  advice  is  a  safe  one. 

(2)  Rivers  generally  run  into  the  sea. 

4.  Give  the  contrapositive  of: 

(1)  No  one  is  altogether  reliable. 

(2)  Every  mistake  is  not  a  proof  of  ignorance. 

5.  Give  the  inverse  of: 

(1)  He  that  bridleth  his  tongue  is  greater  than  he  that 
taketh  a  city. 

(2)  Natives  alone  can  stand  the  climates  of  Africa. 


CHAPTER  X 

CATEGORICAL  ARGUMENTS. 

The  Problem  of  the  Chapter.  In  the  previous 
cnapters  we  have  studied  mainly  the  three  following 
problems:  (1)  the  nature  of  simple  assertion  or 
the  judgment,  (2)  the  logical  expression  of  these 
judgments  or  the  proposition,  and  (3)  the  problem 
of  logical  implication.  In  the  next  two  chapters, 
we  shall  still  be  occupied  with  judgments  and  their 
propositions;  and,  although  the  new  problems  that 
are  to  come  before  us  are  more  complex  than  those 
we  have  studied,  they  will  appear  simpler,  because 
everyone  may  be  presumed  to  have  already  some 
acquaintance  with  them.  The  fact  of  common  ex- 
perience that  underlies  the  topics  of  these  chapters 
is,  that  we  connect  statements  of  various  kinds  with 
one  another  in  numerous  ways,  and  that  we  do 
this  with  a  view  to  making  other  assertions  that,  it 
seems  to  us,  could  not  be  made  as  surely  in  any  other 
way.  Often  the  actual  statements  we  make  are  not 
debatable,  they  are  readily  accepted  by  the  person  to 
whom  we  are  speaking,  and  may,  therefore,  be  re- 
garded merely  as  reminding  him  of  certain  points 
of  common  agreement;  and  if,  beyond  this  simple 
function,  they  have  any  use,  this  must  be  found  m 
what  they  suggest,  and  not  in  what  they  actually 
state.  In  other  words,  we  are  accustomed  to  use 
certain  significant  statements  for  the  purpose  of 

(297) 


298  A  TEXT-BOOK  OF  LOGIC 

making  them  the  bases  of  certain  other  significant 
statements  which  we  wish  the  person  to  whom  we 
are  speaking  also  to  accept.  Now  it  is  quite  obvious 
that  about  such  a  general  fact  as  this  we  may  ask 
whether  there  are  any  rules  of  procedure  that  may 
be  followed,  if  the  suggested  truth  is  to  be  accepted. 
We  may  ask,  that  is,  whether  there  are  any  service- 
able ways  of  connecting  statements  when  these  are 
used  as  the  basis  of  others  the  truthfulness  of  which 
we  wish  particularly  to  recommend.  This  is  the 
question  we  are  to  consider  in  this  and  the  following 
chapters,  a  question  that  is  technically  known  as  the 
problem  of  the  syllogism.  To  state  the  problem 
somewhat  technically,  we  are  now  to  enter  upon  a 
study  of  the  combination  of  propositions,  and  of  the 
laws  of  their  inter-connection. 

Two  Preliminary  Questions.  Before  taking  up 
the  specific  topics  to  which  the  present  chapter  is 
devoted,  there  are  two  questions  to  which  some  at- 
tention must  in  the  first  place  be  given,  —  a  ques- 
tion about  the  syllogism,  and  a  question  about  the 
particular  kind  of  syllogism  that  we  are  immediately 
concerned  with.  About  the  syllogism  we  may  ask 
whether  it  is  a  problem  that  is  set  by  the  judgment, 
by  the  nature  and  limitations  of  human  thought, 
and  one,  therefore,  that  reveals  the  structure  of  the 
thinking  or  knowing  mind ;  or,  if  this  is  not  the  case, 
whether  it  is  a  problem  that  grows  out  of  our  effort 
to  communicate  what  we  know.  In  the  latter  case, 
the  syllogism  is  not  a  problem  that  is  set  directly 
by  the  judgment,  but  one  that  arises  out  of  the 


CATEGORICAL  ARGUMENTS  299 

nature  of  the  proposition.  Now  it  is  not  possible, 
nor  perhaps  is  it  necessary  or  desirable,  to  enter 
into  a  full  discussion  of  the  question  thus  suggested ; 
but,  because  of  its  bearing  upon  our  understanding 
of  the  nature  and  function  of  the  syllogism,  we  may 
point  out  more  specifically  that  the  question  really 
asks  whether  the  syllogism  is  a  method  by  which  the 
human  mind  thinks  when  it  is  seeking  to  gain  knowl- 
edge; or  whether  it  is  a  method  by  which  we  lay 
bare,  for  ourselves  and  others,  the  grounds  on  which 
our  knowledge  is  supposed  to  rest.  That  is,  we 
are  asking  whether  the  syllogism  is,  as  in  the  one 
case,  an  instrument  for  acquiring  knowledge;  or, 
as  in  the  other,  an  instrument  for  the  exposition  of 
knowledge.  In  making  this  statement  disjunctive, 
we  are  not  to  be  understood  to  mean  that  the  syllo- 
gism may  not  serve  both  functions,  nor  to  deny 
that  the  two  functions  may  be  inter-dependent.  In- 
deed, what  we  have  seen  to  be  true  of  the  relation 
of  the  proposition  to  the  judgment,  namely,  that  the 
former,  being  the  expression  in  words  of  the  latter, 
is  controlled  by  motives  that  grow  out  of  our  desire 
to  communicate  what  we  know,  may  be  expected  to 
be  true  also  of  the  syllogism  —  a  series  of  inter- 
connected propositions  —  in  its  relation  to  the  more 
complex  process  of  reasoning.  The  view  that  the 
syllogism  is  a  method  by  which  we  expound  and 
communicate  the  knowledge  that  is  acquired  by 
reasoning  seems  to  have  a  high  degree  of  probability, 
and  it  may  be  allowed,  in  the  main,  to  determine 
our  discussions  in  the  following  sections.  From  this 


300  A  TEXT-BOOK   OP  LOGIC 

point  of  view,  the  syllogism  will  come  before  us  as  a 
series  of  problems  connected  with  the  nature  and 
connection  of  propositions,  and  we  must  consider 
the  present  chapter  as  a  continuation  of  those  imme- 
diately preceding  it  in  which  we  were  developing  the 
character  of  prepositional  statements. 

Turning  now  to  the  second  inquiry,  we  may 
raise  the  question  whether  we  are  to  study  in  this 
chapter  the  connection  between  any  kinds  of  state- 
ment, and  any  kinds  of  connection  between  state- 
ments. The  answer  to  both  parts  of  the  question 
must  be,  No.  There  are  forms  of  statement  that, 
so  long  as  these  forms  are  retained,  do  not  belong 
to  logic  at  all.  We  pointed  this  out  above  when  we 
were  studying  imperatives,  inter rogatives,  optatives, 
and  exclamations.  There  are  also,  as  we  have  seen, 
forms  of  logical  statement  that  are  not  categorical, 
and  which,  as  we  shall  see  later,  present  problems 
quite  distinct  from  those  that  are.  Such,  for  ex- 
ample, are  the  hypothetical  and  disjunctive  prop- 
ositions. We  exclude  from  the  scope  of  this  chap- 
ter both  classes  of  statement,  and  consider  only 
the  relationships  that  hold  between  categorical 
propositions.  There  are  also  kinds  of  connection 
between  categorical  statements  that  are  not  logical 
in  the  restricted  sense  in  which  we  are  using  the 
word  here.  Such,  for  instance,  are  the  connections 
between  ideas  that  the  psychologist  discusses  under 
the  head  of  association.  Such,  also,  are  the  con- 
nections between  ideas  based  upon  the  mathematical 
principle  of  proportion:  A  is  greater  than  B,  B  is 


CATEGORICAL  ARGUMENTS  301 

greater  than  C,  therefore,  A  is  greater  than  C. 
Whatever  the  logical  character  of  these  cases  may 
be,  they  do  not,  on  any  strict  interpretation,  belong 
to  the  present  chapter  which  is  confined  to  a  study 
of  the  connection  of  categorical  propositions  which 
is  illustrated  in  the  Aristotelian  syllogism. 

Nature  of  the  Syllogism.  We  may  describe  a 
syllogism  as  a  series  of  three  propositions  which  are 
related  to  each  other  in  such  a  way  that  the  truth 
expressed  in  one  of  them,  called  the  conclusion,  de- 
pends upon  the  truth  expressed  in  the  other  two, 
called  the  premises,  taken  together.  Let  us  -illus- 
trate this  statement  in  the  following  simple  case: 

All  insects  are  arthropods. 
All  bees  are  insects. 
All  bees  are  arthropods. 

In  this  syllogism,  there  are  three  inter-related  prop- 
ositions, each  one  of  which  has  been  written  sepa- 
rately. It  is  obvious  to  first  inspection  that  the 
truth  of  the  last  written  statement,  'All  bees  are 
arthropods/  avowedly  rests  upon  the  truth  of  the 
other  two  taken  together.  That  is  to  say,  the  truth 
of  every  conclusion  is  a  truth  that  rests  upon  a  con- 
nection of  facts  that  it  requires  two  propositions, 
at  least,  completely  to  express. 

Our  understanding  of  this  type  of  argument  will 
be  facilitated  if  we  learn  to  think  about  the  syllo- 
gism from  the  standpoint  of  the  conclusion  it  states, 
and  not  from  the  standpoint  of  the  premises  it  ex- 
presses. The  reason  for  doing  so  is  found  in  the 


302  A   TEXT-BOOK   OF  LOGIC 

nature  of  the  thought  processes  themselves.  In 
these  processes,  as  we  saw  when  studying  the  judg- 
ment, emphasis  is  laid  primarily  upon  the  answer 
to  the  cognitive  question,  What  is  it?  and  only  sub- 
ordinate importance  is  attached  to  the  method  by 
which  the  answer  is  reached.  Whether  the  process 
of  thought  is  relatively  simple  or  complex,  sub- 
stantive emphasis  is  laid  upon  the  solutions  that 
are  found  to  the  problematic  situations  that  stim- 
ulate the  judging  activity,  and  it  is  the  function 
of  the  conclusions  of  syllogisms  to  express  such 
solutions.  From  this  point  of  view,  the  premises 
must  be  looked  upon  as  expressing  the  grounds  of 
the  fact  or  truth  stated  in  the  conclusion  of  the 
syllogism.  Indeed,  it  is  only  as  stating  the  grounds 
of  what  is  expressed  in  the  conclusion  that  the  prem- 
ises are  premises  at  all.  In  like  manner,  a  con- 
clusion can  be  a  conclusion  only  if  it  is  regarded  as 
the  statement  of  a  grounded  assertion.  The  grounds 
of  assertion  may  be  relatively  simple  as  in  our  judg- 
ments of  perception;  they  may  be  relatively  com- 
plex, as  in  the  syllogism;  but  every  judgment  is  a 
grounded  assertion,  and  when  such  assertions  are 
referred  to  their  grounds,  when,  that  is,  the  reason 
for  holding  the  assertions  is  in  any  way  appealed  to, 
such  assertions  are  properly  called  conclusions. 
Premises  and  conclusions  are  thus  correlative  terms, 
and  can  be  understood  only  from  the  standpoint  of 
their  mutual  implication. 

Further  light  is  thrown  upon  the  nature  of  the 
syllogism  if  we  recall  that  the  mental  process  under- 


CATEGORICAL  ARGUMENTS  303 

lying  the  syllogism  is  a  process  of  reasoning.  The 
mental  process  underlying  the  proposition,  as  we 
have  seen,  is  called  a  judgment.  When,  for  example, 
we  discern  the  aspects  in  which  objects  differ  from, 
and  are  like,  each  other,  directly,  that  is,  by  having 
the  objects  before  us  and  comparing  the  one  with 
the  other,  this  mental  process,  involving  discrim- 
ination, abstraction,  and  synthesis,  is  called  judg- 
ing, and  the  mental  attitude  in  which  the  results  of 
such  a  process  is  asserted  is  called  a  judgment.  Now 
the  mental  process  underlying  the  syllogism  is  not 
essentially  different  from  that  underlying  the  judg- 
ment. Like  the  judgment,  reasoning  rests  upon  com- 
parison, but  unlike  it,  there  is  no  means  of  direct 
comparison  of  one  object  with  another.  In  this 
case,  we  compare  each  of  the  objects  we  are  trying 
to  relate  with  a  third  object  in  order  to  detect 
whether  they  have  anything  in  common  with  it. 
That  is,  we  compare  objects,  through  the  observed 
likeness  or  difference  that  each  has  to  a  third.  This 
is  called  indirect  comparison,  and  the  process  of 
reasoning  in  which  this  is  carried  out  is  called  me- 
diate reasoning.  In  contrast  to  the  so-called  imme- 
diate reasoning  or  judgment,  mediate  reasoning  is 
a  process  underlying  the  Aristotelian  syllogism,  and 
we  may  call  the  stated  results  of  such  a  process  an 
argument.  It  is  such  an  argument  that  gets  ex- 
pressed in  the  syllogism. 

Structural  View  of  the  Syllogism.  We  may,  now, 
point  out  certain  characteristics  of  the  syllogism 
that  are  conditioned  by  the  fact  that  it  is  composed 


304  A  TEXT-BOOK   OF  LOGIC 

of  a  series  of  interrelated  propositions.  Proposi^ 
tions,  for  instance,  may  be  said  to  bear  the  same 
relation  to  the  syllogism  that  terms  do  to  the  prop- 
osition, that  is,  they  may  be  regarded  as  its  con- 
stituent elements.  But  as  terms  do  not  form  prop- 
ositions by  being  brought  together  by  the  copula, 
so,  we  may  say,  the  syllogism  is  not  built  up  by 
the  union  of  propositions.  The  propositions  of  a 
syllogism  express  distinguishable  features  of  a 
complex  process  of  thinking,  and  it  is  the  purpose 
of  the  syllogism  to  make  clear  the  inter-connection 
between  the  several  aspects  of  our  thoughts-about- 
things.  In  other  words,  the  movement  of  thought 
in  syllogistic  reasoning  turns  upon  a  common  ele- 
ment represented  in  the  syllogism  by  the  middle- 
term,  and  it  is  only  through  this  common  element 
that  there  exist  grounds  for  the  truth  of  any  medi- 
ated judgment.  From  this  point  of  view,  the  middle 
term  is  as  characteristic  a  feature  of  the  syllogism 
as  the  copula  is  of  the  proposition. 

Certain  other  features  of  the  syllogism  come  into 
prominence  when  we  consider  it  from  the  stand- 
point of  its  structure.  For  instance,  every  syllo- 
gism has  three  and  only  three  propositions,  —  the 
conclusion,  and  two  premises.  The  conclusion  is  a 
statement  of  the  relation  between  two  terms  which 
are  named,  from  the  place  they  occupy  in  the  syllo- 
gism, the  major  and  minor  terms.  The  subject 
1  (S)  of  the  conclusion  is  the  minor  term  of  the  syl- 
llogism,  and  the  predicate  (P)  of  the  conclusion  is 
jthe  major  term  of  the  syllogism.  Since  now  the 


CATEGORICAL  ARGUMENTS  305 

premises  of  a  syllogism  are  propositions,  they  also 
state  a  relationship  between  terms,  but  not  a  rela- 
tionship between  any  terms.  Their  function  is  to 
state  the  relationship  that  the  major  and  minor 
terms  have  respectively  to  a  common  or  middle 
term  (M).  The  proposition  that  states  the  rela- 
tionship between  the  major  and  middle  terms  is 
known  as  the  major  premise.  The  proposition  thall 
states  the  relationship  between  the  minor  and  the! 
middle  terms  is  known  as  the  minor  premise.  Ill 
should  be  observed  that  the  nature  and  validity  of 
categorical  arguments  do  not  depend  upon  the  order 
in  which  the  propositions  are  named,  but  upon  the 
connection  between  the  propositions  of  which  they 
are  comprised.  It  is  usual,  however,  to  write  the 
major  premise  first,  the  minor  premise  second,  and 
the  conclusion  last. 

With  these  facts  in  mind,  it  is  possible  to  give  a 
definition  of  the  syllogism  that  emphasises  the  con- 
nection of  the  elements  that  are  always  present  in 
these  kinds  of  arguments.  From  this  point  of  view, 
the  syllogism  is  a  method  by  which  we  relate  two 
terms  (S  and  P)  through  the  relation  that  each  has 
to  a  common  or  middle  term  (M). 

Rules  of  the  Syllogism.  In  the  previous  section, 
we  pointed  out  that  the  syllogism  has  a  definite 
structure  which  is  determined  by  the  fact  that  its 
three  constituent  propositions  are  related  to  each 
other  through  a  middle  term.  The  rules  of  the  syl- 
logism may  be  classified  with  respect  to  these  facts, 

20 


306  A   TEXT-BOOK   OF  LOGIC 

-with  respect  to  the  terms,  and  with  respect  to 
the  propositions  of  the  syllogism.  With  respect  to 
its  terms,  the  rules  are  definitely  rules  of  distribu- 
tion. With  respect  to  its  propositions,  the  rules 
refer  to  the  quantity  and  quality  of  the  propositions. 

RULES   OF  DISTRIBUTION 

I.  The  middle  term  must  be  distributed  in  one, 
at  least,  of  the  premises. 

II.  If  a  term  is  distributed  in  the  conclusion,  it 
must  have  been  distributed  in  one  of  the  premises. 

The  reason  for  the  first  rule  is,  that  the  validity 
of  the  syllogism  depends  upon  the  reference  of  the 
major  and  minor  terms  unambiguously  to  the  same 
common  term,  and  this  is  done  with  certainty  only 
if  the  middle  term  is  distributed,  at  least,  once.  If 
the  middle  term  is  undistributed  in  each  premise, 
the  major  term  might  be  related  to  one  part  in  the 
major  premise,  and  the  minor  term  to  another  part 
in  the  minor  premise.  Whenever  this  is  the  case, 
we  have  four  and  not  three  terms  in  the  two  prop- 
ositions, and  thus  the  syllogistic  character  of  the 
argument  is  destroyed.  For  example,  from  the 
statements  that  'All  rash  men  are  confident,'  and 
'All  brave  men  are  confident/  we  cannot  conclude 
that  'All  brave  men  are  rash/  for  the  reason  that 
the  confidence  that  each  has  is  or  might  be  a  differ- 
ent kind  of  confidence;  there  is,  in  other  words,  no 
middle  term  or  common  factor  to  serve  as  a  basis 
of  comparison.  If,  however,  the  middle  term  is  dis- 
tributed in  one,  at  least,  of  the  premises,  the  part 


CATEGORICAL  ARGUMENTS  307 

of  the  term  denoted  by  the  undistributed  middle  in 
the  other  premise  is  included  in  this  distribution, 
and  there  is  thus  a  common  basis  of  comparison  for 
the  major  and  minor  terms.  Thus,  we  can  affirm 
that  'No  Americans  are  Englishmen'  on  the  ground 
that  'All  Englishmen  are  Europeans/  and  'No  Amer- 
icans are/  The  fallacy  involved  in  breaking  the 
rule  for  the  distribution  of  the  middle  term  is  called 
the  fallacy  of  Undistributed  Middle. 

The  reason  for  the  second  rule  is,  that  we  must 
not  make  a  statement,  in  the  conclusion,  about  a 
determinate  number  of  the  objects  denoted  by  a 
term  when,  in  the  premises,  our  statement  has  been 
about  an  indeterminate  number  of  these  objects.  In 
other  words,  we  must  not  go  beyond  our  accepted 
facts.  Stated  conversely,  to  support  a  conclusion 
which  denotes,  in  either  of  its  terms,  a  determinate 
number  of  the  objects  to  which  the  term  applies 
requires  that  all  these  objects  shall  have  been  denoted 
in  one  of  the  premises.  When  this  rule  is  not  ob- 
served by  the  major  term,  the  fallacy  that  results  is 
an  Illicit  Process  of  the  Major,  and  when  it  is  not 
observed  by  the  minor  term  an  Illicit  Process  of  the 
Minor  Term. 

RULES  OF  QUALITY 

I.  If  the  conclusion  is  affirmative,  both  prem- 
ises are  affirmative ;  and  conversely. 

II.  If  the  conclusion  is  negative,  one  premise, 
and  only  one,  is  negative;  and  conversely. 

In  discussing  these  rules,  which  refer  to  the 
relation  of  identity,  or  of  non-identity,  of  two 
classes,  on  the  ground  of  their  identity  or  non- 


308  A  TEXT-BOOK   OF  LOGIC 

identity  with  a  third,  it  is  important  to  observe  that 
we  can  argue  a  relation  of  identity  only  on  the  basis 
of  an  identity  of  relation,  and  a  relation  of  non- 
identity  only  on  the  basis  of  a  non-identity  of  rela- 
tion. In  other  words,  the  relation  of  S  and  P  to  M 
must  be  either  so  far  identical  as  to  warrant  the 
statement  of  the  complete  or  partial  identity  of  S 
and  P;  or  so  far  non-identical  as  to  warrant  the 
statement  of  the  complete  or  partial  non-identity 
of  S  and  P.  If  the  conclusion  is  a  statement  of 
identity,  the  grounds  for  such  a  statement  cannot 
be  found  in  a  relation  of  non-identity;  nor  can  we 
find  grounds  for  a  statement  of  non-identity  in  a 
relation  of  identity.  Hence,  if  the  conclusion  is 
affirmative  both  the  premises  must  be  of  the  same 
quality ;  and  if  the  conclusion  is  negative,  one  of  the 
premises  must  be  of  that  quality. 

Why  can  we  not  ground  any  statement  upon  two 
negative  propositions?  Because,  in  that  case,  there 
is  no  identity  of  relation  between  S  and  M  and  P  and 
M,  on  which  to  base  such  a  statement.  From  the  ex- 
clusion of  both  S  and  P  from  M,  we  cannot  argue 
to  the  identity  of  S  and  P,  nor  can  we  argue  to  the 
non-identity  of  S  and  P.  Two  negative  premises 
cannot,  therefore,  support  any  conclusion,  nor  can 
any  conclusion  be  inferred  from  them. 

RULES   OF  QUANTITY 

I.  A  particular  conclusion  cannot  be  supported 
by  two  particular  premises. 

II.  If  a  conclusion  is  particular,  one,  and  only 
one,  of  the  premises  supporting  it  can  be  particular. 


CATEGORICAL  ARGUMENTS  309 

With  regard  to  the  first  rule,  let  us  suppose  that 
the  particular  affirmative,  and  the  particular  neg- 
ative, conclusions,  SiP  and  SoP,  can  be  supported  by 
two  particular  propositions.  In  the  former  case,  the 
premises  must  be  both  particular  affirmative,  and 
then  the  middle  term  is  undistributed  whichever 
place  it  occupied  in  the  premises.  This  would  give 
the  fallacy  of  the  undistributed  middle.  In  the  sec- 
ond case,  one  premise  must  be  particular  affirmative, 
and  the  other  particular  negative,  and  then  there 
can  be  only  one  distributed  term,  namely,  the  pred- 
icate of  the  negative  premise.  If  this  is  the  middle 
term,  the  major  term  will  be  of  wider  extent  in  the 
conclusion,  which  is  a  negative  proposition,  than  in 
the  major  premise,  —  the  fallacy  of  illicit  process  of 
the  major.  If,  on  the  other  hand,  the  middle  term 
is  not  the  predicate  term  of  the  negative  premise, 
the  argument  fails  on  account  of  the  fallacy  of  undis- 
tributed middle. 

With  regard  to  the  second  rule,  the  particular 
conclusion  must  be  either  affirmative  or  negative. 
If  it  is  affirmative,  the  premises  will  both  be  par- 
ticular affirmative,  II.,  that  is,  propositions  whose 
terms  are  all  undistributed.  A  syllogism  whose 
premises  were  both  particular  affirmative  would  be 
fallacious  on  account  of  undistributed  middle.  If, 
on  the  other  hand,  the  conclusion  were  particular 
negative,  one  of  the  premises  would  have  to  be  par- 
ticular negative,  01,  10,  that  is,  propositions  only 
one  of  whose  terms  is  distributed.  If  this  were  the 
middle  term,  then,  all  the  other  terms  being  undis- 
tributed, the  conclusion  being  negative  would  involve 


310  A  TEXT-BOOK  OF  LOGIC 

the  syllogism  in  an  illicit  process  of  the  major;  and 
if  that  term  were  not  the  middle  term,  the  syllogism 
would  involve  an  undistributed  middle.  Only  one 
premise,  therefore,  of  a  particular  conclusion  can 
be  particular. 

Figures  of  the  Syllogism,  The  propositions  that 
together  constitute  the  premises  or  grounds  of  a 
syllogism  are  characterised,  as  we  have  seen,  by  the 
fact  that  they  have  a  common  or  middle  term.  Now 
since  each  premise  has  two  terms,  a  subject  term 
and  a  predicate  term,  and  one  of  these  is  the  middle- 
term  of  the  syllogism,  it  is  obvious  that  the  middle 
term  may  be  either  the  subject  term  or  the  pred- 
icate term  of  the  major  premise,  and  either  the 
subject  term  or  the  predicate  term  of  the  minor 
premise.  That  is  to  say,  the  middle  term  of  a  syl- 
logism may  occupy  four  different  positions  in  the 
propositions  which,  when  taken  together,  are  the 
premises  of  the  argument  which  the  syllogism  is 
the  means  of  stating.  Now  the  fact  that  the  middle 
term  of  a  syllogism  may  occupy  different  positions 
in  the  premises  of  different  arguments  is  referred 
to  by  the  term  Figure.  The  Figure  of  a  syllogism, 
in  brief,  is  determined  by  the  position  of  the  middle 
term  in  its  major  and  minor  premises. 

The  number  of  Figures  depends  upon  the  num- 
ber of  different  positions  that  the  middle  term  may 
occupy  alternately  in  the  premises  of  a  syllogism. 
Theoretically,  there  are  four.  Thus : 

1.  The  middle  term  may  be  the  subject  term 
of  the  major,  and  the  predicate  term  of  the  minor 
premise. 


CATEGORICAL  ARGUMENTS 


311 


2.  The  middle  term  may  be  the  predicate  term 
of  each  premise. 

3.  The  middle  term  may  be  the  subject  term 
of  each  premise. 

4.  The  middle  term  may  be  the  predicate  term 
of  the  major,  and  the  subject  term  of  the  minor 
premise. 

In  the  order  named,  the  syllogisms  whose  form 
corresponds  to  the  alternative  possibilities  just 
named  are  said  to  be  in  the  First  Figure,  the  Second 
Figure,  the  Third  Figure,  and  the  Fourth  Figure  re- 
spectively. Written  in  outline,  syllogisms  in  these 
Figures  will  present  the  following  appearance: 


First 
Figure 


S— P 


Second 
Figure 

P-# 

S— $£, 

S— P 


Third 
Figure 

M— P 

M— S 

S— P 


Fourth 
Figure 

P— M 

M— S- 

S— P 


As  an  aid  to  the  retention  of  the  positions  of 
the  middle  terms  in  each  of  the  Four  Figures,  we 
may  add  the  following  suggestion.  If  we  connect 
by  a  line  the  middle  terms  of  the  premises  in  the 
Four  Figures  as  just  shown  in  outline,  we  shall 
get  this  result: 


II 

M 


M 


III 

M 


M 


312 


A  TEXT-BOOK   OF  LOGIC 


The  upper  point  of  these  lines  is  the  position  occu- 
pied by  the  middle  term  of  the  major  premise,  and 
the  lower  point  of  the  lines  is  the  position  occupied 
by  the  middle  term  of  the  minor  premise  in  the 
Four  Figures  respectively.  If  now  to  these  lines 
we  add  dotted  lines  to  represent  the  major  and 
minor  premises,  our  diagram  will  assume  this  as- 
pect: 


M 


III 

M 


M/ 


A  diagram  like  this,  of  course,  may  mean  something 
or  nothing  according  as  the  student  can  bring  to  it 
an  interpreting  idea.  A  student  informed  me  that, 
for  a  number  of  a  class  in  logic,  the  two  end  figures 
were  thought  of  as  snakes  fighting  or  hissing  at 
each  other.  The  two  middle  figures  were  thought 
of  as  people  sitting  back  to  back  because  they  were 
cross  with  each  other.  As  this  information  came 
to  me  two  years  after  the  course  was  taken,  it  may 
be  presumed  to  have,  for  one  at  least,  some  mne- 
monic value. 

Special  Rules  of  the  Four  Figures,  Each  of  the 
Four  Figures  has  its  own  special  rules,  which  are 
applications  of  the  general  rules  of  the  syllogism  to 
the  specific  form  that  categorical  arguments  as- 
sume in  these  Figures.  We  shall  state  and  prove 
the  rules  for  each  Figure  in  order. 


CATEGORICAL  ARGUMENTS  313 

FIRST   FIGURE 

RULE  1.     The  minor  premise  must  be  affirmative. 

Let  us  suppose  the  minor  is  negative.  Then, 

M — P      the  major  must  be   affirmative,   and  the 

S — M       conclusion  negative.    Therefore,  the  major 

term  will  be  undistributed  in  the  major 

S — P        premise,  and  distributed  in  the  conclusion ; 

illicit  process  of  the  major.     Hence,  the 
minor  premise  cannot  be  negative,   and  must  be 
affirmative. 
RULE  2.     The  major  premise  must  be  universal. 

If  the  minor  premise  is  affirmative,  the 
middle  term  is  undistributed,  and  must, 
therefore,  be  distributed  in  the  major 
premise.  And  since  the  middle  term  is 
subject  of  this  premise,  the  proposition 
must  be  universal. 

SECOND  FIGURE 

RULE  1.     One  premise  must  be  negative. 

Since  the  middle  term  is  the  predicate  of 
P — M  each  premise,  one  of  the  premises  must  be 
S — M  a  negative  proposition  to  avoid  the  fallacy 

of  undistributed  middle. 

S— P 

RULE  2.     The  major  premise  must  be  universal. 

The  major  term  being  the  predicate  of  a 
negative  proposition  in  the  conclusion,  is 
distributed.  It  must,  therefore,  be  dis- 
tributed in  the  major  premise.  But  since 


314  A  TEXT-BOOK   OF  LOGIC 

there  it  is  the  subject  of  the  proposition, 
the  major  premise  must  be  universal. 

THIRD   FIGURE 

RULE  1.     The  minor  premise  must  be  affirmative. 
Let  us  suppose  that  the  minor  is  negative. 
Then,  the  major  premise  must  be  affirm- 
ative, and  the  conclusion  negative.    There- 
fore, the  major  term  will  be  undistributed 
S — P        in  the  major  premise,  being  the  predicate 
of  an  affirmative  proposition,  and  distrib- 
uted in  the  conclusion,  being  the  predicate  of  a  neg- 
ative   proposition.      This    involves    illicit    major. 
Hence,  the  minor  premise  must  be  affirmative. 

RULE  2.     The  conclusion  must  be  particular. 

Since  the  minor  premise  is  affirmative,  the 
minor  term,  being  predicate,  is  undistrib- 
uted, and  must,  therefore,  be  undistributed 
in  the  conclusion  also.  But  the  minor  term 
is  the  subject  of  the,  conclusion  which, 
therefore,  must  be  particular. 

FOURTH   FIGURE 

RULE  1.     If  either  premise  is  negative,  the  major 

is  universal. 

P — M      If  either  premise  is  negative,  the  conclu- 
M — S      sion  is  negative,  and  the  major  term  of  the 

conclusion  must  be  distributed.     It  must, 

S — P       therefore,    be    distributed    in    the    major 

premise.    But  since  there  it  is  the  subject, 
the  premise  must  be  universal. 


CATEGORICAL  ARGUMENTS  315 

RULE  2.  If  the  major  premise  is  affirmative,  the 
minor  must  be  universal. 
If  the  major  premise  is  affirmative,  its 
middle  term  is  undistributed.  It  must, 
therefore,  be  distributed  in  the  minor 
premise.  And  since  there  the  middle  term 
is  the  subject,  the  premise  must  be  uni- 
versal. 

RULE  3.  If  the  minor  premise  is  affirmative,  the 
conclusion  is  particular. 
If  the  minor  premise  is  affirmative,  the 
minor  term  is  undistributed.  In  the  con- 
clusion, therefore,  this  term  must  be  un- 
distributed. The  conclusion,  therefore,  is 
particular. 

RULE  4.     If  the  minor  premise  is  negative,  both 
premises  are  universal. 
If  the  minor  premise  is  negative,  the  minor 
term   is  distributed.     It  must,  therefore, 
be  distributed  in  the  conclusion  which  will 
then  be  universal.     But  a  universal  con- 
clusion requires  two  universal  premises. 
The  Moods  of  the  Syllogism.      If    now    we    con- 
sider the  structure  of  the  syllogism  from  the  point 
of  view  of  the  quantity  and  quality  of  the  proposi- 
tions which  enter  into  it,  we  meet  with  the  facts 
which  are  denoted  by  the  term  —  the  Moods  of  the 
syllogism.    By  the  Moods  of  the  syllogism  is  meant 
the  character  of  a  syllogism  as  determined  by  the 
quantity  and  quality  of  its  constituent  propositions. 
There  are,  as  we  have  seen,  four  categorical  prop- 


316  A   TEXT-BOOK   OF  LOGIC 

ositions,  SaP,  SeP,  SiP,  SoP,  and  any  combination 
of  three  of  these,  theoretically,  may  form  the  con- 
stituent propositions  of  a  syllogism.  For  example, 
a  syllogism  may  have  in  its  premises  and  conclusion 
only  universal  affirmative  propositions.  But  it  may 
have  in  its  major  premise  a  universal  affirmative,  in 
its  minor  premise  a  universal  negative,  and  in  its 
conclusion  a  universal  negative  proposition.  Every 
syllogism  must  express  itself  by  the  use  of  the  four 
categorical  propositions  three  at  a  time,  and,  there- 
fore, no  syllogism  can  fail  to  have  a  Mood.  That  is 
to  say,  each  of  the  constituent  propositions  of  a  syl- 
logism has  both  a  quantity  and  a  quality,  and  when 
we  have  named  the  quantity  and  quality  of  each 
proposition,  in  the  order  of  major  premise,  minor 
premise,  and  conclusion,  we  have  named  the  Mood 
of  the  syllogism.  Thus,  in  the  examples  just  used, 
the  mood  of  the  first  is  said  to  be  AAA,  that  of  the 
second,  AEE. 

The  Valid  Moods  of  the  Syllogism.  The  Mood  of 
a  syllogism,  we  have  said,  is  determined  by  the 
quantity  and  quality  of  its  constituent  propositions. 
The  question  that  now  comes  before  us  is,  How  many 
of  the  possible  combinations  of  three  out  of  the  four 
categorical  propositions,  taken  as  major  and  minor 
premise  and  conclusion,  will  give  us  valid  moods, 
that  is,  syllogisms  whose  conclusions  logically  de- 
pend upon  the  premises  on  which  they  are  said  to 
rest?  In  answering  this  question,  it  will  simplify 
our  task  if,  leaving  the  conclusions  out  of  consider- 
ation, we  ascertain  the  combinations  of  propositions 


CATEGORICAL  ARGUMENTS  317 

which  are  possible  as  premises.  Since,  as  we  have 
seen,  there  are  four  categorical  propositions,  each 
of  these  may  serve  successively  as  the  major  prem- 
ise of  a  syllogism,  and  each  may  serve  successively 
as  the  minor  premise  of  the  same  syllogism.  Thus, 
writing  the  major  premise  first  and  the  minor  sec- 
ond, we  shall  get  the  following  sixteen  combina- 
tions : 

AA  EA  IA  OA 

AE  EE  IE  OE 

AI  El  II  01 

AO  EO  IO  OO 

If,  now,  we  examine  this  list  of  possible  prem- 
ises, it  is  apparent  that  some  must  be  rejected  by 
the  rules  of  the  syllogism  that  we  have  stated  in 
another  section.  Certain  combinations  are  disqual- 
ified because  they  violate  the  rule  against  negative 
premises,  for  example,  EE,  EO,  OE,  and  00;  cer- 
tain others  must  be  eliminated  because  they  offend 
against  the  rule  about  particular  premises,  for  ex- 
ample, II,  10,  and  01.  There  remain,  after  the  dis- 
qualified members  have  been  eliminated,  the  follow- 
ing combinations : 

AA  EA  IA  OA 

AE  IE 

AI  El 

AO 

These  we  must  consider  as  the  only  premises  that 
can  be  appealed  to  in  support  of  any  conclusion 
which  we  may  be  concerned  to  maintain. 


318  A   TEXT-BOOK   OF   LOGIC 

Relation  of  Moods  to  Figure.  There  is,  however, 
a  further  question  that  requires  an  answer,  namely, 
whether  we  can  throw  the  defence  of  a  conclusion 
upon  any  of  the  above-mentioned  premises  in  any 
of  the  Figures  without  affecting  the  validity  of  the 
argument.  Or,  to  state  the  same  question  con- 
versely, Is  each  of  the  above  pairs  of  premises  ca- 
pable of  rendering  a  valid  conclusion  in  each  of  the 
Four  Figures?  We  are  asking,  what  effect,  if  any, 
the  statement  of  a  syllogism  in  either  of  the  Four 
Figures  has  upon  the  validity  of  the  argument. 

There  are  two  methods  that  may  be  adopted  in 
seeking  an  answer  to  this  question.  And  first  we 
shall  examine  each  of  the  above  combinations  of 
premises  in  the  light  of  the  special  rules  of  each 
Figure,  accepting  those  that  conform,  and  rejecting 
those  that  do  not  conform  to  the  requirements  of  the 
particular  Figure. 

In  the  First  Figure,  the  major  premise  must  be 
universal,  and  the  minor  affirmative.  The  only  com- 
binations of  premises  that  stand  these  tests  are,  AA, 
AI,  EA,  and  El.  If  we  draw  the  proper  conclusion 
in  each  case,  we  may  write  the  four  valid  moods 
for  this  figure  as  follows : 

AAA  All  EAE  EIO 

It  will  be  observed  that  in  this  figure  we  are  able 
to  support  by  premises  a  conclusion  stated  in  any 
one  of  the  four  propositions  A,  E,  I,  and  O. 

In  the  Second  Figure,  the  major  premise  must 
be  universal,  and  one  premise  negative.  The  only 


I 

CATEGORICAL  ARGUMENTS  319 

combinations  of  premises  that  satisfy  these  require- 
ments are  AE,  AO,  EA,  and  EL  With  their  respect- 
ive conclusions,  these  premises  give  the  following 
Moods : 

AEE  AGO  EAE  EIO 

The  conclusions  in  the  Second  Figure,  it  will  be  ob- 
served, are  negative  propositions,  either  E  or  0. 

In  the  Third  Figure,  the  minor  premise  must  be 
affirmative,  and  the  conclusion  particular.  The  fol- 
lowing are  the  combinations  of  premises  in  which 
the  minor  is  affirmative :  AA,  AI,  EA,  El,  IA,  and 
OA.  From  each  of  these  we  may  draw,  as  required, 
particular  conclusions,  and  the  valid  Moods  will  be 
as  follows: 

AAI         All         EAO         EIO         IAI         OAO 

In  the  Fourth  Figure,  if  either  premise  is  neg- 
ative, the  major  is  universal;  if  the  major  premise 
is  affirmative,  the  minor  is  universal;  if  the  minor 
premise  is  affirmative,  the  concluson  is  particular, 
and  if  the  minor  is  negative,  both  premises  are  uni- 
versal. The  only  combinations  of  propositions 
which  satisfy  these  conditions  are:  AA,  AE,  EA, 
El,  IA.  To  draw  conclusions  from  these  premises, 
we  must  remember  that  when,  in  this  figure,  the 
minor  premise  is  affirmative,  the  conclusion  must  be 
particular.  The  valid  moods  are : 
I 

AAI  AEE  EAO  EIO  IAI 


320  A  TEXT-BOOK   OF  LOGIC 

In  this  figure,  we  may  support  conclusions  stated  in 
each  of  the  four  propositions,  excepting  the  univer- 
sal affirmative. 

The  second  method  of  determining  the  valid 
Moods  is  to  examine  each  of  the  combinations  of 
premises  in  each  Figure,  and  observe  whether  it 
satisfies  the  requirements  of  a  valid  argument. 
Since  we  have  eliminated  those  combinations  of 
premises  which  do  not  meet  the  rules  of  quantity 
and  quality  as  stated  above,  the  validity  of  the  argu- 
ment will  depend  upon  its  satisfying  the  rules  of 
distribution.  We  shall  give  examples  below  foryall 
the  Figures,  and  the  student  is  urged  to  work  out 
the  entire  list.  This  will  be  a  review  exercise,  and 
it  will  help  him  to  fix  definitely  the  .essentials  con- 
nected with  the  Figure  and  Mood  of  syllogisms,  and 
the  distrbution  of  terms. 

To  begin,  we  may  write  the  structural  formulae 
for  the  Figures  in  which  we  are  to  examine  the  given 
combination  of  premises.  Thus: 

I  II  III  IV 

M-^-P  P— M  *          M— P  P— M 

S— M  S— M      '       M— S  M— S 


S— P  S— P  S— P  S— P 

In  the  vacant  spaces  of  each  premise  may  be  written 
the  combination  of  premises  we  are  wishing  to  ex- 
amine, and  in  the  vacant  space  of  the  conclusion, 
the  conclusion  that  these  premises  support. 

When  this  has  been  done,  our  first  question  will 
be :    Is  the  middle  term  distributed  in  one,  at  least, 


CATEGORICAL   ARGUMENTS  321 

of  the  premises?  The  second  question  will  be:  Is 
each  distributed  term  of  the  conclusion,  when  there 
is  one,  distributed  also  in  one  of  the  premises? 

We  give  the  following  examples  chiefly  as  a 
guide  to  the  student  in  working  out  the  entire  list. 
AE  in  all  the  Figures. 

I  II  III  IV 

MaP  PaM  MaP  PaM 

SeM  SeM  MeS  MeS 


SeP  SeP  SeP  SeP 

In  the  First  Figure,  this  argument  is  invalid  be- 
cause the  major  term  is  distrbuted  in  the  conclusion 
and  is  not  distributed  in  the  major  premise:  Illicit 
process  of  the  major. 

In  the  Second  Figure  the  argument  is  valid. 

In  the  Third  Figure  the  argument  is  invalid  be- 
cause the  major  term  is  distributed  in  the  conclusion 
and  is  not  distributed  in  the  major  premise :  Illicit 
process  of  the  major. 

In  the  Fourth  Figure,  the  argument  is  valid. 
AI  in  all  the  Figures. 

I  n  III  IV 

MaP  PaM  MaP  PaM 


SIM  SdM     I          MiS  MiS 


SiP  ^Sf  SiP  Si3 

In  the  First  Figure,  the  argument  is  valid. 

In  the  Second  Figure,  the  argument  is  invalid 
because  the  middle  term  is  not  distributed  in  either 
premise  :   Undistributed  middle. 
21 


322  A  TEXT-BOOK   OF  LOGIC 

In  the  Third  Figure,  the  argument  is  valid. 

In  the  Fourth  Figure,  the  argument  is  invalid 
because  the  middle  term  is  not  distributed  in  either 
premise:  Undistributed  middle. 

REFERENCES 
H.  A.  Aikins,  The  Principles  of  Logic,  Chs.  XII.,  XIII.,  XIV., 

XV.,  XVI. 
J.   E.   Creighton,   An   Introductory   Logic,   3d   Edition,   Chs. 

VIII.,  IX. 
J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Part  I.,  Chs. 

XV.,  XVI. 
W.   S.  Jevons,  Elementary  Lessons  in   Logic,  Lessons  XV., 

XVI. 
J.  N.  Keyes,  Formal  Logic,  2d  Edition,  Part  III.,  Chs.  I.,  III., 

V. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  VI. 
W.  Minto,  Logic,  Inductive  and  Deductive,  Part  IV.,  Chs.  I., 

II.,  III.,  IV. 

C.  Read,  Logic,  Deductive  and  Inductive,  Chs.  IX.,  X. 
W.  J.  Taylor,  Elementary  Logic,  Chs.  IX.,  XI. 

ADVANCED 

F.  H.  Bradley,  The  Principles  of  Logic,  Book  I.,  Chs.  III., 

VII.,  VIII. 
W.  R.  B.  Gibson,  The  Problem  of  Logic,  Chs.  XXL,  XXII., 

XXIIL,  XXIV.,  XXV. 
H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Chs.  XII.,  XIII., 

XIV. 

H.  Lotze,  Logic,  Vol.  I.,  Book  I.,  Ch.  III. 
J.  S.  Mill,  A  System  of  Logic,  Book  II.,  Chs.  II.,  III. 
P.  C.  S.  Schiller,  Formal  Logic,  Chs.  XIV.,  XV.,  XVI. 
C.  Sigwart,  Logic,  Vol.  I.,  Part  II.,  Ch.  III.,  §§  54,  55,  59. 
J.  Venn,  Empirical  Logic,  Ch.  XV. 
J.  Welton,  A  Manual  of  Logic,  Vol.  I.,  Book  IV.,  Chs.  I.,  II., 

III. 


CATEGORICAL  ARGUMENTS  323 

QUESTIONS 

1.  In  what  respects  are  the  problems  of  this  and  the  im- 
mediately following  chapters  related  to  those  of  the  pre- 
ceding chapters? 

2.  What  general  view  of  the  syllogism  is  assumed  in  the 
discussions  of  this  chapter? 

3.  What  particular  forms  of  statement  are  and  what  are 
not  studied  in  this  chapter? 

4.  Discuss  the  advantages  and  disadvantages  of  viewing 
the  syllogism  from  the  standpoint   (1)   of  its  premises 
and    (2)    of  its  conclusion? 

5.  What  mental  process  underlies  the  syllogism,  and  how 
does  it  differ  from  that  which  underlies  the  judgment? 

6.  What  do  you  understand  by  the  major,  minor  and  mid- 
dle terms  of  the  syllogism? 

7.  Define  the   syllogism   from  the  standpoint  of  its   con- 
tained terms. 

8.  Define  and  illustrate  the  following:     Premise,  Conclu- 
sion, Major  premise,  Minor  premise,  Undistributed  mid- 
dle, Illicit  process. 

9.  With  respect  to  what  aspects  of  its  contained  proposi- 
tions are  the  rules  of  the  syllogism  determined? 

10.  Explain  why  the  middle  term  of  a  syllogism  must  be 
distributed  in  at  least  one  of  the  premises. 

11.  Why  is  there  no  separate  rule  relating  to  a  term  in  the 
conclusion  that  is  undistributed? 

12.  Why  must  the  premises  of  an  affirmative  conclusion  be 
affirmative? 

13.  Explain  why  a  negative  conclusion   can  be  supported 
only  if  but  one  of  its  premises  is  negative. 

14.  Why  cannot  a  particular  conclusion  be  supported  by  two 
particular  premises? 

15.  What  is  meant  by  the  Figure  of  a  syllogism? 

16.  Describe  the  formal  characteristics  of  each  of  the  Fig- 
ures. 

17.  What  do  you  understand  by  the  Special  Rules  of  the 
Four  Figures? 


324  A  TEXT-BOOK   OF  LOGIC 

18.  What  is  meant  by  the  Moods  of  the  syllogism? 

19.  How  do  you  determine  all  the  theoretically  valid  Moods 
of  the  syllogisms? 

20.  What  is  the  relation  of  the  Moods  to  the  Figures  of  the 
syllogism? 

21.  What  two  methods  may  be  adopted  to  determine  whether 
a  particular  argument  is  valid  in  a  given  Figure? 

EXERCISES 

NOTE  —  Write  the  formula  for  each  proposition  and  syl- 
logism in  your  answers  to  the  following  questions. 

1.  Point  out  (1)  the  conclusion,   (2)  the  middle  term,   (3) 
the  major  term,  (4)  the  minor  term,  (5)  the  major  pre- 
mise,   (6)    the   minor   premise   in   the   following   argu- 
ments : 

(1)  The  receiver  of  stolen  property  should  be  punished; 
you  have  received  stolen  property,  and,  therefore, 
should  be  punished. 

(2)  Theft  is  crime;  theft  was  encouraged  by  the  laws 
of  Sparta,  therefore,  the  laws  of  Sparta  encouraged 
crime. 

(3)  Only  those  messages  which  have  been  prepaid  will 
be  delivered;  this  message  has  been  prepaid,  and, 
therefore,  will  be  delivered. 

2.  Name  all  the  rules  of  the  syllogism  which  are  broken 
by  each  of  the  following  Moods: 

AIA,     EEI,     IEA,     101,     IIA,     AEI. 

3.  Prove  from  the  rules  alone,  irrespective  of  Figure,  that 
IE  can  yield  no  valid  conclusion. 

4.  In  what  Figures  do  the  following  premises  yield  a  valid 
conclusion : 

AA,     AI,     EA,     OA. 

5.  Why  cannot  a  particular  negative  proposition  stand  (1) 
as  a  premise  in  the  First,  (2)  as  a  major  in  the  Second, 
(3)  as  a  minor  in  the  Third,  or  (4)  as  a  premise  in  the 
Fourth  Figure? 


CATEGORICAL  ARGUMENTS  325 

6.  Arrange  the  following  arguments  in  the  order  of  major 
and  minor  premise,  and  conclusion,  and  determine  their 
Figure,  Mood,  and  validity: 

(1)  All  colours  are  physical  phenomena,  but  no  sounds 
are  colours,  and  therefore  no  sound  is  a  physical 
phenomenon. 

(2)  Whatever  is  given  on  the  evidence  of  sense  may  be 
taken  as  a  fact;  the  existence  of  God,  therefore,  is 
not  a  fact,  for  it  is  not  evident  to  sense. 

(3)  Every  candid  man  acknowledges  merit  in  a  rival; 
every  learned  man  does  not  do  so;  therefore,  every 
learned  man  is  not  candid. 

7.  What  can  be  determined  respecting  a  syllogism  under 
each  of  the  following  conditions: 

(1)  That  only  one  term  is  distributed,  and  that  only 
once. 

(2)  That  only  one  term  is  distributed,  and  that  twice. 

(3)  That  two  terms  only  are  distributed,  each  only  once. 

(4)  That  two  terms  are  distributed,  each  twice. 


CHAPTER  XI 
OTHER  FORMS  OF  CATEGORICAL  ARGUMENT 

Their  Relation  to  the  Syllogism.  The  syllogism 
may  be  considered  from  either  of  two  points  of  view, 
from  the  point  of  view  of  its  premises,  or  from  the 
point  of  view  of  its  conclusion.  If  we  attend  par- 
ticularly to  the  premises,  we  shall  think  of  the  syllo- 
gism as  a  method  by  which  from  given  data  we 
arrive  at  a  conclusion;  if  we  attend  particularly  to 
the  conclusion,  we  shall  think  of  the  syllogism  as  a 
method  by  which  we  state  the  grounds  on  which 
a  position  already  arrived  at  is  held  to  rest.  These 
two  ways  of  regarding  the  syllogism  are  not  con- 
tradictory, nor  is  our  view  of  the  nature  of  the  syl- 
logism affected  by  the  possibility  of  this  two-fold 
approach  to  its  problems.  There  results  only  a 
slightly  different  emphasis  in  one's  exposition;  in 
the  one  case,  the  conclusion,  in  the  other,  the  prem- 
ises, come  to  be  the  focus  of  our  logical  interest. 

The  reason  why  we  may  alter,  in  the  way  just 
indicated,  our  exposition  of  the  syllogism  is  that  the 
syllogism  does  not  express  a  series  of  consecutive 
steps  by  which  the  judgment  actually  proceeds  for- 
ward from  data  to  conclusion,  or  backward  from 
conclusion  to  grounds;  but  it  represents,  in  a  con- 
ventional form  and  order,  the  simplest  inter-connec- 
tions of  a  complex  process  of  reasoning.  It  is  some- 
times brought  forward  as  an  objection  to  syllogistic 

(326) 


OTHER  FORMS   OF  CATEGORICAL  ARGUMENT     327 

reasoning  that  it  is  not  an  instrument  of  the  dis- 
covery of  truth ;  but  the  objection  rests  upon  a  mis- 
understanding. The  truth  about  any  subject-matter 
is  discovered  by  thinking,  and  the  syllogism  is  not, 
and  does  not  affect  to  be,  a  substitute  for  thinking. 
We  may  even  say  that  unless  truth  already  exists, 
unless  some  kind  and  degree  of  thinking  has  taken 
place,  the  syllogism  has  no  function  to  perform. 
The  syllogism  presupposes  the  existence  of  truth, 
and  is  not  the  condition  of  its  existence.  It  repre- 
sents the  results  of  our  reflection  upon  the  truth 
that  is  already  in  our  possession,  —  a  reflection  that 
is  directed  towards  finding  out  the  reasons  why 
truth  assumes  a  demonstrative  character.  Now  this 
is  not  a  small  nor  an  easy  thing.  It  is,  however,  an 
eminently  practical  thing.  For  when  thought  takes 
itself  to  task,  and,  by  reflection  upon  its  own  proc- 
esses, demands  that  the  conditions  of  truth  be 
erected  into  principles  of  demonstration,  we  may  be 
led  to  see  how  far  from  being  demonstrative  are 
many  of  the  beliefs  that  we  hold  most  confidently. 

These  remarks  have  a  practical  bearing  upon 
the  subjects  of  this  chapter,  and  may  prepare  us  to 
understand  why  our  thoughts-about-things  can  be 
thrown  into  a  variety  of  forms  which  conform  in 
principle  only  to  the  Aristotelian  syllogism.  The 
discussion  of  these  arguments  should  lead  us  to  see 
that  even  in  logic  we  are  not  bound  in  the  state- 
ment of  our  thought  to  the  formal  primness  of  the 
three-term  syllogism. 


328  A  TEXT-BOOK  OF  LOGIC 

Enthymeme.  This  is  the  name  of  a  categorical 
argument  which  omits,  in  statement,  one  of  the  con- 
stituent factors  of  the  syllogism.  Now  since  there 
are  three  propositions,  two  premises  and  a  con- 
clusion, in  a  categorical  syllogism,  the  omission  of 
either  one  of  these  from  the  syllogism  results  in  an 
enthymeme.  But  it  must  not  be  supposed  that  the 
omission  of  one  member  of  a  syllogism  destroys  the 
syllogistic  character  of  the  reasoning,  for,  as  the 
term  itself  implies,  the  omitted  member  still  func- 
tions in  the  mind  of  the  person  who  states  his 
thought  in  this  particular  form.  The  enthymeme, 
consequently,  is  a  particular  way  of  stating  a  cat- 
egorical argument,  it  is  not  a  new  form  of  categor- 
ical syllogism. 

According  as  the  omitted  member  of  the  syllo- 
gism is  the  major  premise,  the  minor  premise,  or 
the  conclusion,  the  resulting  enthymeme  is  said  to 
be  of  the  First  Order,  the  Second  Order,  and  the 
Third  Order  respectively.  An  enthymeme  of  the 
First  Order,  consequently,  is  a  syllogism  which  is 
abbreviated  by  the  omission  of  the  major  premise. 
For  example,  Those  who  have  no  occupation  have 
nothing  in  which  to  interest  themselves,  and  are, 
therefore,  unhappy.'  An  enthymeme  of  the  Second 
Order  is  a  syllogism  which  is  abbreviated  by  the 
omission  of  the  minor  premise.  For  example,  Those 
who  have  no  occupation  are  unhappy,  because  they 
have  nothing  in  which  to  interest  themselves.'  An 
enthymeme  of  the  Third  Order  is  a  syllogism  which 
is  abbreviated  by  the  omission  of  the  conclusion. 


OTHER  FORMS  OF  CATEGORICAL  ARGUMENT   329 

For  example,  'Those  who  have  nothing  in  which  to 
interest  themselves  are  unhappy,  and  those  who 
have  no  occupation  have  nothing  in  which  to  interest 
themselves/ 

In  the  enthymeme,  as  in  the  fully  expressed 
syllogism,  the  order  in  which  the  propositions  are 
stated  is  wholly  a  matter  of  convenience,  and  does 
not  affect  the  nature  or  validity  of  the  argument.  In 
case  of  the  enthymeme,  however,  it  must  be  made 
obvious  by  the  use  of  such  words  as  'and,'  'because/ 
and  'therefore,'  which  members  of  the  syllogism  we 
are  undertaking  to  express. 

It  may  be  questioned  whether  the  enthymeme 
has  both  Mood  and  Figure.  Perhaps  the  best 
answer  to  this  inquiry  would  be  that  a  syllogism  in 
any  Figure  and  Mood  may  be  stated  as  an  enthy- 
meme by  the  omission  of  one  of  its  constituent  prop- 
ositions. But  since  Mood  and  Figure  are  character- 
istics of  arguments  only  when  fully  expressed  in  the 
three-term  syllogism,  the  most  that  we  can  say  is 
that  an  enthymeme  implies  a  Figure  and  Mood,  and 
not  that  it  has  either. 

Polysyllogism.  In  the  enthymeme,  we  have  an 
example  of  the  elliptical  character  of  thought.  Think- 
ing,  indeed,  is  ordinarily  carried  on  by  means  of  the 
smallest  number  of  factors  necessary  to  its  success 
definitely  present  to  consciousness.  When  the 
thought  is  a  simple  one,  and  the  inter-connection  of 
its  parts  consists  of  a  relation  of  three  terms,  any 
one  of  the  relations  may  fall  into  the  background 
without  invalidating  or  making  doubtful  its  truth. 


330  A  TEXT-BOOK   OF  LOGIC 

This  is,  as  we  have  seen,  the  case  of  the  enthymeme. 
When,  however,  thinking  becomes  complex,  and  the 
inter-connection  of  its  parts  involves  relations  of 
many  terms,  it  is  much  more  necessary  to  simplify 
our  methods,  if  thinking  is  not  to  break  down  under 
the  weight  of  the  terms  into  which  the  subject- 
matter  of  thought  is  analysed.  In  this  case,  what 
we  do  is  to  build  up  a  series  of  enthymemes  or 
abbreviated  syllogisms,  and  such  a  series  is  called 
a  polysyllogism.  A  polysyllogism  is,  therefore,  a 
series  of  inter-connected  enthymemes  representing  a 
continuous  chain  of  reasoning. 

It  is  customary  to  denote  the  syllogisms  into 
which  a  polysyllogism  may  be  analysed  by  the  terms 
prosyllogism  and  episyllogism.  The  application  of 
these  terms  depends  entirely  upon  whether  we  are 
thinking  of  the  constituent  syllogisms  in  the  for- 
ward direction,  that  is,  of  the  first  syllogism  as 
being  connected  with  the  second,  and  the  second 
with  the  third,  etc. ;  or  whether  we  are  thinking  of 
them  in  the  reverse  order,  that  is,  of  the  second 
syllogism  as  being  connected  with  the  first,  the 
third  with  the  second,  etc.  When  we  think  of  the 
constituent  syllogisms  in  the  former  way,  each  syl- 
logism is  called  a  prosyllogism;  and  when  we  think 
of  them  in  the  latter  way,  each  syllogism  is  called 
an  episyllogism.  The  terms  prosyllogism  and  epi- 
syllogism, consequently,  are  used  relatively,  and  any 
syllogism  in  a  train  of  reasoning  may  be  both  a  pro- 
and  an  episyllogism.  It  is  obvious  that  the  first 


OTHER  FORMS  OF  CATEGORICAL  ARGUMENT    331 

syllogism  in  such  a  series  can  be  only  a  prosyllogism, 
and  the  last  only  an  episyllogism. 

Types  of  Polysyllogism  Trains  of  reasoning 
of  the  type  just  described  fall  into  two  main  classes, 
progressive  and  regressive.  We  shall  describe  each 
of  these  briefly,  and  merely  for  the  purpose  of  show- 
ing their  logical  structure. 

A  progressive,  synthetic,  or  episyllogistic  train 
of  reasoning  proceeds  from  the  premises  of  a  pro- 
syllogism  to  the  conclusion  of  an  episyllogism.  A 
polysyllogism  of  this  character  develops  progress- 
ively the  consequences  of  the  premises  which  form 
its  starting  point.  Stated  otherwise,  the  progressive 
polysyllogism  advances  from  the  conditions  to  what 
is  conditioned,  from  causes  to  effects.  Probably 
the  most  familiar  illustrations  of  this  class  of  poly- 
syllogism for  the  student  are  to  be  found  in  the 
direct  proofs  of  geometrical  propositions.  A  re- 
gressive, analytic,  or  prosyllogistic  train  of  reason- 
ing proceeds  from  the  conclusion  of  an  episyllogism 
to  the  premises  of  a  prosyllogism.  In  such  cases 
we  go  back  from  a  conclusion  to  show  the  grounds 
upon  which  it  rests.  Stated  otherwise,  we  are  said 
to  reason  from  the  conditioned  to  its  necessary  con- 
ditions, from  effects  to  causes. 

Illustrations  of  these  two  classes  of  polysyllo- 
gisms  will  be  found  in  the  following  sections  in  which 
we  consider  the  various  forms  that  such  trains  of 
reasoning  may  assume.  In  this  and  the  preceding 
section  we  have  been  considering  the  general  charac- 
teristics of  a  group  of  syllogisms;  in  the  sections 


332  A   TEXT-BOOK   OF  LOGIC 

that  follow  we  are  to  study  the  cases  that  fall  under 
one  or  other  of  the  two  main  classes  of  the  group. 

Sorites.  This  is  a  polysyllogism  whose  constitu- 
ent syllogisms  are  all  in  the  First  Figure,  and  from 
which  all  the  conclusions,  except  the  last,  are  omit- 
ted. Or,  since  a  syllogism  which  omits  one  of  its 
propositions  is  an  enthymeme,  we  may  regard  a 
sorites  as  a  series  of  enthymemes  from  each  of 
which,  except  the  first,  one  premise  is  omitted,  and 
from  each  of  which,  except  the  last,  the  conclusion 
is  omitted. 

There  are  two  forms  of  sorites,  progressive  and 
regressive,  which  are  usually  distinguished  as  the 
Aristotelian  and  the  Goclenian  respectively.  An  ex- 
amination of  each  of  these  will  serve  to  set  the 
nature  of  this  class  of  arguments  more  clearly  in 
the  light. 

An  Aristotelian  sorites  is  a  progressive  series  of 
enthymemes  in  which  the  omitted  conclusion  of  each 
prosyllogism  forms  the  minor  premise  of  the  suc- 
ceeding episyllogism.  A  familiar  example  may  be 
taken  from  Rom.  VIII.,  29,  30 :  'For  whom  he  fore- 
knew, he  also  foreordained  to  be  conformed  to  the 
image  of  his  Son,  .  .  .  and  whom  he  foreordained, 
them  he  also  called;  and  whom  he  called,  them  he 
also  justified:  and  whom  he  justified,  them  he  also 
glorified/  A  Goclenian  sorites — so  called  from  Pro- 
fessor Goclenius  of  Marburg  (1547-1628)  its  dis- 
coverer —  is  a  regressive  series  of  enthymemes  in 
which  the  omitted  conclusion  of  each  prosyllogism 
forms  the  major  premise  of  the  succeeding  episyl- 


OTHER  FORMS  OF  CATEGORICAL  ARGUMENT    333 

logism.  For  example:  'One  must  take  pains  if  he 
is  to  be  a  successful  man;  industry  is  necessary  to 
taking  pains ;  health  is  necessary  to  industry ;  a  reg- 
ulated diet  and  sufficient  recreation  and  rest  are 
necessary  to  health ;  and,  therefore,  a  regulated  diet 
and  sufficient  recreation  and  rest  are  necessary  if 
one  is  to  become  a  successful  man/ 

The  symbolic  expression  and  analysis  of  each 
of  these  forms  of  sorites  may  be  given  thus : 

ARISTOTELIAN   SORITES  GOCLENIAN    SORITES 

S  is  A  Z  is  P 

A  is  B  Y  is  Z 

B  is  C  X  is  Y 

C  is  P  S  is  X 


S  is  P  S  is  P 

Analysis : 

S  is  A  )  Z  is  P  ^| 

A  is  B  C  Y  is  ^  I 

f  (S  is  B)  )  ('(Y  is  P)J 

•j  B  is  C  J  Z  is  Y 

(  (S  is  C)  -)  (  (X  is  P;"| 

C  is  P  C  S  is  X  V 

S  is  P  )  S  is  P  J 


Each  of  these  forms  is  subject  to  special  rules 
which  we  shall  proceed  to  state  and  prove, 
l 

THE  SPECIAL  RULES  OF  THE  ARISTOTELIAN  SORITES 

RULE  1.  Only  one  premise,  and  that  the  last, 
can  be  negative. 

Let  us  suppose  that  two  of  the  premises  are  neg- 
ative. Then  the  conclusion  of  the  syllogism  in 


334  A   TEXT-BOOK   OF   LOGIC 

which  the  first  negative  premise  occurs  will  be  neg- 
ative. But  since  this  negative  conclusion  is  neces- 
sarily a  premise  of  the  next  succeeding  syllogism, 
its  concluson  will  be  negative,  and  so  on,  until  a 
negative  conclusion  enters  as  a  premise  into  a  syl- 
logism which  has  the  second  negative  premise.  But 
as  we  have  seen,  from  two  negative  premises  no 
conclusion  can  be  inferred.  Only  one  premise,  there- 
fore, can  be  negative. 

This  negative  premise  must  be  the  last.  Let  us 
suppose  that  some  other  premise  is  negative.  In 
that  case,  the  conclusion  of  the  syllogism  into  which 
it  entered  would  be  negative.  This  conclusion,  serv- 
ing as  the  minor  premise  of  the  following  episyllo- 
gism,  would  give  a  conclusion  that  is  negative,  that 
is,  one  in  which  the  major  term  is  distributed.  But 
since  the  major  term  in  the  affirmative  major  prem- 
ise is  undistributed,  the  argument  would  fail  on  ac- 
count of  an  illicit  process  of  the  major.  No  premise, 
therefore,  except  the  last  can  be  negative. 

RULE  2.  Only  one  premise,  and  that  the  first, 
can  be  particular. 

Since  every  premise,  except  the  last,  must  be 
affirmative,  it  is  evident  that  the  conclusions  of  the 
constituent  syllogisms,  except  the  last,  must  be 
affirmative.  If  now  the  first  premise  is  particular, 
the  conclusion  of  the  first  prosyllogism  will  be  par- 
ticular. And  if  any  other  premise,  except  the  first, 
were  particular,  there  would  occur  somewhere  in  the 
series  two  particular  affirmative  premises,  and  this, 


OTHER  FORMS  OF  CATEGORICAL  ARGUMENT    335 

in  the  First  Figure,  involves  the  fallacy  of  undis- 
tributed middle. 

THE  SPECIAL  RULES  OF  THE  GOCLENIAN  SORITES 

RULE  1.  Only  one  premise,  and  that  the  first, 
can  be  negative. 

If  more  than  one  premise  were  negative,  one  of 
the  constituent  syllogisms  would  be  involved  in  the 
fallacy  of  negative  premises.  And  since,  if  any 
premise  is  negative,  the  conclusion  must  be  negative, 
that  premise  must  be  the  one  which  contains  the 
predicate  term  of  the  conclusion,  that  is,  the  first 
premise  in  this  particular  case. 

RULE  2.  Only  one  premise,  and  that  the  last, 
can  be  particular. 

If  any  premise  is  particular,  the  conclusion  of 
the  syllogism  in  which  it  occurs  would  be  particular ; 
and  if  this  conclusion  became  a  premise  of  another 
syllogism  whose  premise  was  already  particular, 
there  would  be  involved,  in  the  First  Figure,  the  fal- 
lacy of  undistributed  middle.  Only  the  last  premise, 
therefore,  can  be  particular. 

Epicheirema.  This  is  a  regressive  chain  of 

reasoning  in  which  one,  or  both,  of  the  premises  is 
expanded  by  the  addition  of  a  reason.  In  other 
words,  it  is  an  argument  in  which  one  of  the  prem- 
ises is  an  enthymeme,  but  in  which  both  may  be. 
If  only  one  of  the  premises  is  supported  by  a  reason, 
the  epicheirema  is  called  single,  and  when  both  are 
so  supported,  double.  A  single  epicheirema,  there- 


336  A  TEXT-BOOK  OF  LOGIC 

fore,  is  a  regressive  chain  of  reasoning  in  which 
one  of  the  premises  is  supported  by  a  reason.  For 
example : 

All  rational  beings  are  to  be  treated  with  respect,  inas- 
much as  they  are  made  in  the  image  of  God. 
Slaves  are  rational  beings. 
Therefore,  slaves  are  to  be  treated  with  respect. 

— Father  Clarke. 

A  double  epicheirema  is  a  regressive  chain  of 
reasoning  in  which  both  premises  are  supported  by 
a  reason.  For  example : 

All  Malays  are  cruel,  because  all  savages  are. 

All  the  aboriginal  inhabitants  of  Singapore  are  Malays, 

because  all  the  natives  of  that  part  of  Asia  are. 
Therefore,  all  natives  of  Singapore  are  cruel. 

— Welton. 

The  formulae  for  these  two  kinds  of  epicheirema 
may  be  written  as  follows : 

SINGLE  DOUBLE 

Every  M  is  P,  because  it  is  X  Every  M  is  P,  because  it  is  X 

Every  S  is  M  Every  S  is  M,  because  it  is  Y 

Every  S  is  P  Every  S  is  P 

REFERENCES 

J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Ch.  X. 

J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Part  I.,  Ch. 
XVIII. 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Lesson  XVIII. 

J.  N.  Keynes,  Formal  Logic,  2d  Edition,  Part  III.,  Ch.  VI. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  VI.,  §§  11-13. 


OTHER   FORMS   OF  CATEGORICAL  ARGUMENT     337 

W.  Minto,  Logic,  Inductive  and  Deductive,  Book  I.,  Part  IV., 

Ch.  V. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Ch.  XI. 
W.  J.  Taylor,  Elementary  Logic,  Ch.  XIII. 

ADVANCED 

W.  R.  B.  Gibson,  The  Problem  of  Logic,  Ch.  XXIX. 
H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Ch.  XVI. 
J.  Welton,  A  Manual  of  Logic,  Vol.  I.,  Book  IV.,  Ch.  VI. 

QUESTIONS 

1.  What   characteristic   of  human   thinking  underlies   the 
forms  of  argument  studied  in  this  chapter? 

2.  What  is  an  Enthymeme? 

3.  Name  and  illustrate  the  distinct  types  of  Enthymeme. 

4.  How  do  we  know  whether  any  expressed  proposition  of 
an  Enthymeme  is  major  or  minor  premise  or  conclusion? 

5.  Do  Enthymemes  have  Figure  and  Mood?     Explain. 

6.  What  is  a  Polysyllogism? 

7.  Under  what  conditions  does  human  thinking  assume  a 
polysyllogistic   form? 

8.  Explain  and  illustrate  the  meaning  of  the  terms  Pro- 
syllogism  and  Episyllogism. 

9.  Describe  and  illustrate  the  general  characteristics  of  a 
Progressive  Polysyllogism.     By  what  other  names  is  it 
known? 

10.  Describe  and  illustrate  the  general  characteristics  of  a 
Regressive  Polysyllogism.     By  what  other  names  is  it 
known? 

11.  What  is  a  Sorites? 

12.  Describe  and  illustrate  the  character  of  an  Aristotelian 
Sorites.     Write  also  its  structural  formula. 

13.  Describe  and  illustrate  the  character  of  a  Goclenian  So- 
rites.   Write  its  structural  formula, 

22 


338  A  TEXT-BOOK  OF  LOGIC 

14.  What  is  an  Epicheirema? 

15.  Explain  and  illustrate  each  type  of  Epicheirema,   and 
write  the  formula. 

EXERCISES 

NOTE  —  Write  the  formula  for  each  of  the  propositions 
and  syllogisms  contained  in  your  answers  to  the  following 
questions. 

1.  What  is  the  logical   character  of  the  following  argu- 
ments : 

( 1 )  He  must  have  committed  the  murder,  for  he  was  the 
only  person  present  with  the  deceased  at  the  time. 

(2)  Nations  are  justified  in  revolting  when  badly  gov- 
erned, for  every  people  has  a  right  to  good  govern- 
ment. 

(3)  Death  cannot  be  an  evil,  for  it  is  universal. 

(4)  The  planet  Mars  resembles  the  earth  in  possessing 
atmosphere,    water,    and    moderate    temperatures, 
and  these  conditions  on  the  earth  are  necessary  to 
its  being  inhabited. 

(5)  He  must  be  mad  to  do  such  a  thing. 

2.  What  is   the  logical   character   of  the   following  argu- 
ments : 

(1)  Misfortunes  sometimes  are  circumstances  tending  to 
improve   character,   circumstances   tending   to   im- 
prove character  are  promoters  of  happiness,  what 
tends  to  promote  happiness  is  for  the  general  well- 
being,    therefore,    misfortunes    sometimes    promote 
general  well-being. 

(2)  A  wise  man  is  one  who  seeks  to  gain  knowledge,  the 
man  who  seeks  to  gain  knowledge  must  be  indus- 
trious, the  industrious  man  has  to  make  sacrifices, 
to  make  sacrifices  is  always  a  hardship,  and,  there- 
fore, a  wise  man  always  lives  a  life  of  hardship. 

3.  Prove  that  in  an  Aristotelian  Sorites  only  the  last  prem- 
ise can  be  negative,  and  only  the  first  particular. 


OTHER   FORMS   OF  CATEGORICAL  ARGUMENT     339 

4.  Construct    an    Aristotelian    Sorites    with    a    particular 
negative  conclusion. 

5.  Prove  that  in  a  Goclenian  Sorites  only  the  last  premise 
can  be  particular  and  only  the  first  negative. 

6.  Construct  a  Goclenian  Sorites  with  a  particular  negative 
conclusion. 

7.  Give  one  example  of  each  class  of  Epicheirema. 


CHAPTER  XII 

DISJUNCTIVE  AND   HYPOTHETICAL   PROPOSITIONS   AND 
ARGUMENTS 

The  Disjunctive  Proposition.  We  have  already 
distinguished  the  various  types  of  logical  proposi- 
tion, and  discussed  their  relation  to  each  other.  We 
have  seen  that  in  the  categorical  proposition  P  is 
affirmed  or  denied  of  S  simply.  The  disjunctive 
proposition,  on  the  other  hand,  is  the  expression  of 
an  alternative  predication.  In  the  disjunctive  prop- 
osition, the  character  of  S  seems  to  waver  between 
a  number  of  alternative  possibilities,  P  or  Q  or  M, 
and  we  are  not  able  to  determine  which  of  these 
really,  or  for  our  purpose,  belongs  to  S.  'S  is  either 
P,  or  Q,  or  M,'  is  a  typical  disjunctive  proposition. 

Before  proceedings  to  the  discussion  of  the  dis- 
junctive syllogism,  there  are  several  questions  about 
the  disjunctive  proposition  which  require  attention. 
And,  first,  we  may  note  that  the  alternatives  which 
form  the  predicates  of  such  a  proposition,  are  not 
any  alternatives,  but  are  usually  alternatives  that 
have  something  in  common.  We  have  met  the  con- 
verse of  this  statement  in  the  chapter  on  division, 
where  we  saw  that  the  species  of  a  genus  were  to  be 
understood  as  a  series  of  alternatives  which  had  a 
common  nature.  What  we  mean  to  express  in  our 
disjunctive  propositions,  is,  therefore,  not  unfa- 
miliar; and  the  formal  statement 'S  is  either  P  or  Q 

(340) 


PROPOSITIONS  AND  ARGUMENTS  341 

or  M'  may  be  interpreted  to  mean  that  P  and  Q  and 
M  are  predicates  which  are,  or  may  be,  contained 
under  the  wider  predicate  R  which  can  be  asserted 
of  S.  For  example,  'He  is  either  a  lawyer,  a  doctor, 
a  teacher,  or  a  clergyman,'  may  be  expressed  in  the 
simpler  statement,  'He  is  a  member  of  a  learned  pro- 
fession/ The  alternatives  of  disjunctive  proposi- 
tions are  usually  of  this  class,  and  fall  within  a 
single  domain  or  universe  of  discourse.  They  con- 
form, as  do  all  other  statements,  to  the  limitations 
of  relevant  assertion.  But  whether  every  instance 
of  alternative  predication  is  actually  thought  of  in 
its  relation  to  a  limiting  universe  is  what  we  cannot 
affirm.  All  we  hold  is  that  logical  alternatives  imply 
a  common  basis,  and  that  it  is  this  common  basis 
that  gives  to  disjunction  its  distinctive  meaning. 

Second,  the  question  whether  the  alternatives  of 
a  disjunction  should  be  treated  as  mutually  exclusive 
or  not  has  aroused  a  good  deal  of  discussion,  and 
there  seems  to  be  no  simple  answer  to  it.  The 
meaning  of  the  question  may  be  made  plain  if  we 
give  it  a  formal  expression.  When  it  is  said  that 
'S  is  either  P  or  Q  or  M,'  is  it  necessarily  implied 
that  S  cannot  be  both  P  and  Q  and  M?  There  can 
be  no  doubt  that  in  a  great  many  instances  the  alter- 
native predicates  do,  as  a  matter  of  fact,  exclude 
each  other.  For  example,  we  may  say  that  'Plato 
was  born  in  either  429  or  427  B.  C.'  About  the  in- 
surrection in  Mexico  we  may  say,  'It  will  either  suc- 
ceed or  be  crushed.'  Some  logicians  maintain  that 
this  is  the  only  sense  in  which  disjunctive  predica- 


342  A  TEXT-BOOK  OF  LOGIC 

tion  can  be  understood  in  logic,  and  that  the  in- 
stances in  which  this  does  not  occur  are  due,  as 
Bradley  says,  to  "our  slovenly  habits  of  expression 
and  thought,"  and  are  "no  real  evidence  against  the 
exclusive  character  of  disjunction."  On  the  other 
hand,  attention  may  be  called  to  the  fact  that  we 
do  express  our  meanings  in  disjunctive  forms  which 
cannot  or  need  not  be  interpreted  in  this  exclusive 
manner.  For  example,  '  He  is  either  a  fool  or  a 
knave'  may  mean  that  he  is  the  one  or  the  other, 
but  it  is  quite  possible  for  a  knave  to  be  a  fool,  and 
a  fool,  a  knave.  In  such  cases  as  this,  where  the 
truth-import  and  the  statement-import  are  not  neces- 
sarily the  same,  we  are  following  the  line  of  least 
error  if  we  choose  the  less  determinate  meaning,  in 
the  absence  of  any  indication  that  the  more  deter- 
minate meaning  is  the  one  intended.  What  the 
statement  *S  is  either  P  or  Q  or  M/  therefore,  means 
is  that  S  cannot  be  neither  P  nor  Q  nor  M ;  it  must 
be  one,  and,  unless  otherwise  indicated,  it  may  be 
more  than  one.  We  must  be  guided  in  our  interpre- 
tation, not  by  the  form  of  the  proposition,  but  by  the 
nature  of  its  subject-matter. 

Third,  the  series  of  alternatives  that  constitute 
the  predicates  of  disjunctive  propositions  must  be 
exhaustive.  That  is,  they  must  determine  com- 
pletely the  alternative  possibilities  in  the  given  in- 
stance. If  we  say  The  water  is  either  hot  or  cold/ 
the  statement  is  misleading,  if  we  assume  that 
all  the  alternatives  of  the  disjunction  are  ex- 
plicitly stated.  But  if  we  say  The  water  is  either 


PROPOSITIONS  AND  ARGUMENTS  343 

hot  or  cold  or  of  some  mean  temperature/  the  state- 
ment is  true,  and,  in  principle,  exhaustive.  It  would 
seem,  therefore,  that  to  secure  an  exhaustive  enu- 
meration of  alternatives  were  more  fundamentally 
important  than  to  make  them  exclusive ;  and  in  any 
case  we  can  say  that  the  latter  is  sometimes  im- 
possible where  the  former  presents  no  particular 
difficulty. 

The  Nature  and  Classes  of  the  Disjunctive  Syllo- 
gism. The  syllogism  whose  major  premise  is  a  dis- 
junctive proposition  is  called  a  disjunctive  syllo- 
gism. The  significance  of  such  a  syllogism  consists 
in  the  fact  that  conclusions  may  be  inferred  from 
premises  that  are  indeterminate  in  content;  or, 
that  the  truth  of  any  proposition  may  rest  upon  a 
number  of  conditions,  one  or  more  of  which  may  be 
undetermined  in  character. 

We  may  distinguish  two  classes  of  disjunctive 
argument,  according  as  the  nature  of  the  subject 
of  the  disjunctive  major  premise  requires  two,  or 
more  than  two,  terms  to  state  exhaustively  the  alter- 
native possibilities.  If  the  major  premise  of  a  dis- 
junctive argument  has  two  alternatives  in  its  pred- 
icate, the  argument  is  called  a  simple  disjunctive 
syllogism;  if  the  predicate  term  of  such  an  argu- 
ment presents  more  than  two  alternatives,  the  argu- 
ment is  called  mixed.  The  reason  for  this  distinc- 
tion is  that  the  character  of  the  other  two  proposi- 
tions of  the  syllogism  is  affected  by  the  consider- 
ations to  which  we  have  adverted.  For  in  such 
arguments  as  we  are  at  present  concerned  with,  it 


344  A  TEXT-BOOK  OF  LOGIC 

is  evident  that  we  can  only  affirm  or  deny  one  or 
more  of  the  alternatives  presented  by  the  major 
premise,  such  affirmation  or  denial  giving  us  the 
minor  premise;  and  deny  or  affirm  the  remaining 
alternative,  or  alternatives,  such  denial  or  affirma- 
tion giving  us  the  conclusion  of  the  syllogism.  Thus, 
the  general  rule  to  which  disjunctive  arguments 
must  conform  is  that  to  affirm  or  deny  one  or  more 
of  the  members  of  a  series  of  alternatives  is  to  deny 
or  affirm  the  remaining  member  or  members.  Now 
if  the  disjunctive  major  premise  presents  only  a 
pair  of  alternatives,  the  minor  premise  and  con- 
clusion of  the  syllogism  are  both  categorical  prop- 
ositions; there  is,  in  other  words,  only  one  disjunc- 
tive premise,  and  that  the  major.  Such  an  argu- 
ment is  called  a  simple  disjunctive  syllogism.  If, 
on  the  other  hand,  there  are  more  than  two  alter- 
natives in  the  disjunctive  major  premise,  one,  or 
both,  of  the  other  propositions  of  the  syllogism  must 
be  disjunctive  also.  In  such  a  case,  we  call  the  argu- 
ment a  mixed  disjunctive  syllogism. 

The  Moods  of  the  Disjunctive  Syllogism.  Each 
class  of  disjunctive  argument  has  two  moods,  de- 
pending upon  whether  the  minor  premise  affirms  or 
denies  one  or  more  of  the  alternatives  presented  by 
the  major  premise.  The  names  of  these  moods, 
like  those  that  we  shall  meet  with  in  our  study  of  the 
hypothetical  syllogism,  are  derived  from  the  Latin 
words  which  denote  the  quality  of  the  propositions 
which  constitute  the  minor  premise  and  conclusion 
respectively.  For  example,  if  the  minor  premise  is 


PROPOSITIONS  AND  ARGUMENTS 


345 


negative,  and  the  conclusion  is  affirmative,  the  mood 
of  the  syllogism  is  called  the  Modus  Tollendo  Ponens, 
that  is,  the  mood  which  by  denying  affirms.  If,  on 
the  other  hand,  the  minor  premise  is  affirmative, 
and  the  conclusion  is  negative,  the  mood  is  called 
the  Modus  Ponendo  Tollens,  that  is,  the  mood  which 
by  affirming  denies.  These  statements  will  be 
understood  if  read  in  connection  with  the  formulae 
for  the  two  classes  of  disjunctive  syllogism  in  each 
of  these  moods  which  follow : 


DISJUNCTIVE   SYLLOGISM 


MOOD 


Ponendo  Tollens 


Modus 
Tollendo  Ponens 


SIMPLE 

A  is  either  B  or  C. 
A  is  B. 


A  is  either  B  or  C. 
A  is  not  B. 
A  is  C. 


MIXED 

A  is  either  B  or  C  or  D. 

A  is  B. 

A  is  not  either  C  or  D. 

A  is  either  B  or  C  or  D 

A  is  not  B. 

A  is  either  C  or  D. 


The  Validity  of  Disjunctive  Arguments.  A  fur- 
ther question  relates  to  the  validity  of  these  moods. 
We  have  seen  that  disjunctive  propositions  are 
required  to  state  their  alternatives  exhaustively, 
that  is,  to  enumerate  alternately  all  the  possibilities 
presented  by  the  subject-matter  under  consideration. 
We  have  also  seen  that  in  some  cases  the  alternatives 
are  at  the  same  time  exclusive,  that  is,  incompat- 
ible. Thus,  'A  is  either  B  or  C'  may  mean  (1)  'A 
is  either  B  or  C,  but  not  statedly  both;'  or  it  may 
mean  (2)  'A  is  either  B  or  C,  but  statedly  not  both/ 


346  A  TEXT-BOOK  OF  LOGIC 

that  is,  the  equivalent  of  'A  is  either  B  or  else  C.' 
Now  in  whichever  way  we  understand  the  disjunc- 
tive proposition,  an  argument  based  upon  it  is  valid 
in  Modus  Tollendo  Ponens,  because  all  disjunctive 
arguments  imply  the  presence  in  the  subject  of  one 
or  more  of  the  alternatives  specified  in  the  predicate 
of  the  major  premise.  That  is  to  say,  the  subject 
cannot  be  neither  of  the  predicated  alternatives. 
The  meaning  of  the  subject  professedly  is  to  be 
found  within  the  number  of  enumerated  predicates. 
Hence,  whether  the  predicates  are  exclusive  or  not, 
to  deny  one  or  more  of  a  subject  is  to  bring  the 
subject  nearer  to  one  or  more  of  the  remaining 
predicates.  That  is,  the  Modus  Tollendo  Ponens  em- 
phasises the  exhaustive  character  of  the  disjunctive 
major.  On  the  other  hand,  the  Modus  Ponendo  Tol- 
lens  is  valid  only  when  an  exclusive  reading  of  the 
major  is  understood.  For  example,  when  we  say 
of  any  one  that  'He  is  a  fool  or  a  knave/  we  cannot 
infer  that  because  'He  is  a  fool/  that  'He  is  not  a 
knave/  unless  it  is  distinctly  understood  that  the 
individual  case  precludes  the  possibility  of  him  being 
both.  Thus,  if  we  wish  to  state  this  meaning  unam- 
biguously, we  should  have  to  say  'He  is  either  a  fool 
or  else  a  knave/  thereby  implying  that  he  is  not 
both  together.  When,  therefore,  the  disjunctive 
major  takes  the  form  of  'statedly  not  both  or  all  the 
predicates/  the  Modus  Ponendo  Tollens  is  a  valid 
mood  for  disjunctive  arguments.  This  mood  empha- 
sises the  exclusive  character  of  the  disjunctive 
major. 


PROPOSITIONS  AND  ARGUMENTS  347 

The  Hypothetical  Proposition.  Any  proposition 
which  states  a  connection  between  two  possibilities 
is  hpyothetical.  For  example,  'If  water  is  heated  at 
standard  pressure,  it  will  boil  at  100°  C.'  There  are 
two  characteristics  of  a  hypothetical  proposition  to 
which  attention  should  be  given.  _JThe  firat_is_that 
it  isjhe  form  of  statement  in  which  w_a  express  our 
judgments  when  the  material  of  these  judgments  is 
possible^  not  actual.  This  does  not  mean  that  the 
material  dealt  with  may  not  be  actual,  it  means  only 
that  we  are  not  concerned  with  it  as  existing,  but 
with  the  situations  in  which  it  is  possible  for  it  to 
exist.  Thus,  to  take  the  judgment  which  is  ex- 
pressed in  the  proposition  'If  eggs  are  scarce,  they 
will  be  dear.'  In  this  proposition  we  are  not  assert- 
ing that  'eggs  are  scarce,'  nor  are  we  affirming  that 
'they  are  dear;'  we  are  merely  stating  that  'when- 
ever eggs  are  scarce,  they_  are_  &t_:the  same  time 
dear.'  In  other  words,  we  are  stating  a  connection 
between  'it  is  possible  for  eggs  to  be  scarce,'  and 
'it  is  possible  for  them  to  be  dear.' 

The  second  characteristic  of  hypothetical  prop- 
ositions relates  to  the  kind  of  connection  that  they 
affirm.  This  may  be  brought  out  if  we  regard  the 
judgments  underlying  hypothetical  statements  to  be 
concerned  with  the  development  of  the  consequences 
that  follow  from  a  supposition.  What  leads  to  the 
erection  of  a  supposition  is,  doubtless,  some  feature 
of  an  actually  existing  situation  which  cannot  be 
brought  under  direct  observation;  but  the  supposi- 
tion itself  is  not  part  of  the  situation  in  the  same 


348  A  TEXT-BOOK  OF  LOGIC 

sense  that  the  feature  itself  is.  Any  supposition  is  a 
suggestion  which  is  based  upon  a  wider  range  of  ex- 
perience than  the  circumstances  which  calls  it  forth, 
and  we  fall  back  upon  this  broader  experience  to 
guide  us  in  dealing  with  a  situation  that  is  proble- 
matical. Now  problematic  situations  can  be  de- 
veloped only  in  a  series  of  possibilities,  and  possi- 
bilities are  expressed  in  hypothetical  propositions: 
'If  A  is  B,  it  is  C.'  The  part  of  the  hypothetical 
proposition  which  states  the  supposition  or  condition 
is  called  the  antecedent,  the  part  which  states  the 
result  of  the  supposition  is  called  the  consequent. 

is  thus  affirmed  by  hypothet- 


ical propositions  is  a  relation  of  dependence  between 
antecedent  and  consequent,  such  Jhflt  the  truth  ?* 

lishment  of  the_  antecedent.  The  hypothetical 
proposition  thus  states  a  rule  under  which  we  may 
bring  for  testing  any  fact  or  situation  about  which 
we  are  at  all  doubtful.  It  should  be  observed  that 
it  is  the  nature  of  the  thought  expressed,  and  not 
the  form  of  the  expression  that  constitutes  any 
proposition  hypothetical.  While  usually  we  intro- 
duce hypothetical  statements  with  'if,'  they  may  be 
prefaced  by  'granted  that/  'suppose  that,'  'allowing 
that,'  'whenever,'  'wherever;'  and  sometimes  there 
is  no  verbal  sign  to  indicate  that  our  thought  is 
hypothetical,  as,  for  example,  'Trespassers  will  be 
prosecuted/  'Deserters  will  be  shot  on  sight/  etc. 

The  Hypothetical  Syllogism.     Any  syllogism  in 
which  the  major  premise  is  a  hypothetical  proposi- 


PROPOSITIONS  AND  ARGUMENTS  349 


a  hypothetical  syllogism.   In  hypothet- 


ical arguments  the  minor  premise  and  the  conclusion 
are  both  categorical  propositions.  Now  since  the 
major  premise  states  a  connection  between  two 
possibilities,  the.  ^jnin^r^premise  must  state  some- 
thing about  one  or  other  of  these  possibilities  cate- 
^gorically  if  there  is  to  be  an  inference.  The  only 
things  that  can  be  stated  are  that  either  of  the  pos- 
sibilities has  or  has  not  been  verified.  Theoretically, 
this  would  give  four  kinds  of  hypothetical  syllo- 
gism, the  minor  premises  of  which  would  affirm  and 
deny  separately  the  antecedent  and  consequent  of 
the  major  premise.  Two  of  these,  however,  fail  to 
give  the  proper  basis  for  an  Inference,  .namely,  when 
minor  premise  HpmVfl  thfii<U^p(V^PT1'<'i  and  when 
consequent.  The  reason  for  the  fail- 


ure is  that  we  are  in  each  case  required  to  go  be- 
yond what  is  contained  in  the  major  premise.  For 
example,  when  we  say  'If  A  is  B,  it  is  C,'  we  are  not 
to  be  understood  to  mean  that  the  only  condition  of 
'A  being  C'  is  that  'A  is  B.'  We  said  above,  for  in- 
stance, that  'If  eggs  are  scarce,  they  are  dear;'  but, 
of  course,  they  may  be  dear  for  other  reasons  as 
well,  —  a  corner  on  the  market  by  the  cold  storage 
interests,  for  example.  Hence,  if  we  were  to  deny 
the  antecedent  of  this  proposition,  'Eggs  are  not 
scarce/  and  use  this  as  a  minor  premise,  we  could 
not  infer  that  'they  are  not  dear.'  .  The  antecedent 
of  a  hypothetical  proposition  states  a  condition,  but 
3bes  not  offer  itself  as  the  sole  condition  of  the 
truth  of  the  consequent.  If,  on  the  other  hand, 


350  A  TEXT-BOOK  OF  LOGIC 

we  were  to  affirm  the  consequent,  'Eggs  are  dear/ 
we  cannot  infer  that  'they  are  scarce/  and  the  rea- 
son is  the  same.  The  forms  of  the  syllogism  are 
reduced,  therefore,  to  two,  in  one  of  which  the 
minor  premise  affirms  the  antecedent  of  the  major, 
and  in  the  other  the  minor  premise  denies  the  con- 
sequent of  the  major.  In  reference  to  these  forms 
of  the  syllogism,  we  may  state  the  general  rule  of 
hypothetical  arguments  as  follows :  When  two  pos- 
sibilities are  related  as  antecedent  and  consequent, 
the  truth  of  the  consequent  follows  from  the  truth 
of  the  antecedent,  and  the  falsity  of  the  antecedent 
follows  from  the  falsity  of  the  consequent. 

The  Moods  of  the  Hypothetical  Syllogism.  Corre- 
sponding to  these  two  forms  of  hypothetical  argu- 
ment we  may  distinguish  two  moods  of  the  syllo- 
gism. There  is  first  the  argument  in  which  the 
minor  premise  affirms  the  antecedent  of  the  major 
premise,  —  the  Modus  Ponens ;  and,  second,  the 
argument  in  which  the  minor  premise  denies  the 
consequent  of  the  major  premise,  —  the  Modus  Tol- 
lens. 

The  antecedent  and  consequent  of  the  major 
premise  of  any  hypothetical  syllogism  may  be  either 
affirmative  or  negative.  In  each  of  the  two  moods, 
therefore,  we  may  distinguish  four  forms  of  hypo- 
thetical argument  as  follows:  (1)  the  antecedent 
and  consequent  of  the  major  premise  may  both  be 
affirmative;  (2)  the  antecedent  may  be  affirma- 
tive, and  the  consequent  negative;  (3)  the  antece- 
dent may  be  negative,  and  the  consequent  affirm- 


PROPOSITIONS  AND  ARGUMENTS  351 

ative;  (4)  both  antecedent  and  consequent  may  be 
negative.  It  will  be  evident  that  arguments  in  these 
moods  will  have  sometimes  an  affirmative  and  some- 
times a  negative  proposition  in  the  minor  premise, 
and  the  same  will  be  true  of  the  conclusion.  The 
names  of  the  several  forms  of  the  moods  of  hypo- 
thetical syllogisms,  like  those  of  the  disjunctive  syl- 
logism, are  derived  from  the  Latin  words  which  de- 
scribe the  quality  of  the  propositions  which  consti- 
tute the  minor  premise  and  the  conclusion.  We 
shall  briefly  characterise  each  mood  and  give  exam- 
ples and  formula  for  the  different  forms  of  the  two 
moods. 

i.  Modus  Ponens, — the  mood  in  which  the  minor 
premise  affirms  the  antecedent  of  the  major  premise, 
and  the  conclusion  affirms  the  consequent.  Argu- 
ments in  this  mood  are  said  to  be  Constructive. 
The  validity  of  arguments  in  this  mood  is  based 
upon  the  fact  that  we  are  bound  to  accept  whatever 
follows  from  any  data  we  have  accepted.  If,  for 
example,  we  accept  as  a  possibility  a  fall  in  temper- 
ature, we  are  bound  to  accept  whatever  is  condi- 
tioned upon  this  possibility,  say,  colder  weather. 
We  may,  therefore,  construct  a  hypothetical  argu- 
ment in  this  mood  as  follows : 

A  fall  in  temperature  means  colder  weather. 
The  temperature  is  falling. 
Therefore,  the  weather  will  be  colder, 


352  A  TEXT-BOOK  OF  LOGIC 

The  different  forms  of  the  Modus  Ponens  are 
given  here  with  illustrations  of  each  form. 

1 i )  Modus  Ponendo  Ponens,  —  the  mood  which  by 

affirming  affirms. 

If  A  is  B,  it  is  C.  If  any  county  increases  in  wealth, 
it  increases  in  power; 

A  is  B,  The  United  States  is  increasing  in 

wealth, 

A  is  C,  Therefore,  the  United  States  is  in- 

creasing in  power. 

(2)  Modus  Ponendo  Tollens,  —  the  mood  which  by 

affirming  denies. 

If  A  is  B,  it  is-not  C.  If  any  import  duty  is  imposed 
simply  for  revenue  purposes,  that 
duty  is  not  protective; 

A  is  B.  The  English  import  duties  are  im- 

posed simply  for  revenue  purposes; 

A  is-not  C.       Therefore,  they  are  not  protective. 

(3)  Modus  Tollendo  Ponens,  —  the  mood  which  by 

denying  affirms. 
If  A  is  not  B,  it  is  C.    If  any  swan  is  not  white,  it  is 

black ; 

A  is-not  B.      Australian  swans  are  not  white, 
A  is  C.  Therefore,  they  are  black. 

(4)  Modus  Tollendo  Tollens,  —  the  mood  which  by 

denying  denies. 

If  A  is-not  B,  it  is-not  C.  If  any  war  is  not  defensive, 
it  is  not  just; 


PROPOSITIONS  AND  ARGUMENTS  353 

A  is-not  B.      The   wars   waged   by   Napoleon   the 

Great  were  not  defensive, 
A  is-not  C.      Therefore,  they  were  not  just. 

2.  Modus  Tollens, — the  mood  in  which  the  minor 
premise  denies  the  consequent  of  the  major  premise, 
and  the  conclusion  denies  ffh^  antPppHpnt  Argu- 
ments in  this  mood  are  said  to  be  Destructive.  The 
validity  of  arguments  in  this  mood  follows  from  the 
relations  expressed  by  the  major  premise.  For  if 
B  follows  of  necessity  from  the  existence  of  A,  — 
'If  A  then  B,' — the  failure  of  B  to  appear  must  mean 
the  absence  or  non-existence  of  /L  An  illustration 
of  an  argument  in  this  mood  is : 

If  no  men  were  mad,  asylumsjwould  be  useless, 
Asylums  are-not  useless, 
Therefore,  s_ome  men  are  mad. 
The  different  forms  of  the  Modus  Tollens  are 
given  here  with  illustrations  of  each  form.^ 

( i )  Modus  Tollendo  Tollens,  —  the  mood  which  by 
denying  denies. 

If  A  is  B,  it  is  C.  If  any  country  is  civilised,  it  has 
a  population  amongst  whom  educa- 
tion is  general; 

A  is-notjC^  The  people  of  Russia  are  not  gener- 
ally educated; 

A  is-not  B.  Therefore,  Russia  is  not  a  civilised 
country. 

V 

23 


354  A  TEXT-BOOK  OF  LOGIC 

(2)  Modus  Ponendo  Tollens,  —  The  mood  which  by 

affirming  denies. 
If  A  is  B,  it  is  not  C.     If  any  social  institution  is 

justifiable,  it  oppresses  no  class  of 

the  community; 
A  is  C.  Slavery  does  oppress  a  class  of  the 

community, 
A  is-not  B.      Therefore,  it  is  not  justifiable. 

(3)  Modus  Tollendo  Ponens,  —  the  mood  which  by 

denying  affirms. 
If  A  is-not  B,  it  is  C.    If  any  railroad  is  not  required 

in  the  district  through  which  it  runs, 

it  is  a  financial  failure; 
A  is-not  C.         The  great  American  lines   are   not 

financial  failures, 
A  is  B.  Therefore,  they  are  required  in  the 

districts  through  which  they  run. 

(4)  Modus  Ponendo  Ponens,  —  the  mood  which  by 

affirming  affirms. 

If  A  is-not  B,  it  is-not  C.  If  any  country  has  no 
capital  invested  abroad,  its  imports 
will  not  exceed  its  exports; 

A  is  C.  England's  imports  do  exceed  her  ex- 

ports, 

A  is  B.  Therefore,  England  has  capital  in- 

vested abroad. 

Dilemmas.  We  come  now  to  the  study  of  dilem- 
mas, a  class  of  arguments  which  combines  in  various 
ways  characteristics  of  the  three  kinds  of  proposi- 


PROPOSITIONS  AND  ARGUMENTS  355 

tion  already  studied,  the  categorical,  the  disjunctive, 
and  the  hypothetical.  The  peculiar  feature  of  a 
dilemmatic  argument  is  that  it  presents  a  choice 
between  two  alternatives.  When  used  for  rhetor- 
ical purposes  these  alternatives  are  of  such  a  kind 
that,  whilst  one  of  them  must  be  accepted,  both  lead 
to  disagreeable  results.  To  force  by  argument  the 
acceptance  of  one  or  other  of  a  pair  of  alternatives 
is  the  chief  function  of  the  dilemma,  and  as  the  re- 
sult of  such  an  argument  an  opponent  is  said  'to  be 
on  the  horns  of  a  dilemma/  Arguments  in  which 
the  choice  rests  among  three  alternatives  are  not 
dilemmas  in  the  strict  definition  of  the  term,  but 
trilemmas,  just  as  those  which  force  a  choice  among 
four  alternatives  are  tetralemmas.  The  principle? 
of  all  these  arguments,  however,  are  the  same,  and 
it  will  be  sufficient  to  study  them  in  connection  with 
the  simplest  forms,  —  the  dilemmas. 

The  dilemma  may  be  defined  as  a  syllogism  with 
a  compound  hypothetical  major  premise  and  a  dis- 
junctive minor.  By  a  compound  hypothetical  prop- 
osition is  meant  one  in  which  there  is  a  plurality 
of  terms  in  either  the  antecedent  or  consequent,  or 
in  both.  The  simplest  form  of  hypothetical  prop- 
osition, we  have  seen,  is  'If  A  is  B,  it  is  C.'  Such 
a  proposition  may  become  compound  by  adding 
terms  to  antecedent  and  consequent.  'If  A  is  B,  it 
is  C  or  D,'  is  a  compound  hypothetical  proposition, 
and  we  must  understand  it  to  mean  'If  A  is  B,  it  is 
C*  and  'If  A  is  B,  it  is  also  D.'  That  is  to  say,  there 
is  no  true  disjunction  in  this  case,  but  only  an  ab- 


356  A  TEXT-BOOK  OF  LOGIC 

breviated  expression  of  two  simple  hypothetical 
propositions.  The  same  remarks  hold  good  also  of 
the  other  forms  that  compound  hypothetical  prop- 
ositions may  assume;  for  example  of,  'If.  _A  is  B  or 
C^iLisJ) ;'  'If  A  is  B  or  C,  it  is  D  or  E.'  Proposi- 
tions of  this  type  form  the  major  premises  of  dilem- 
matic  arguments.  The  reason  why  propositions  of 
this  type  constitute  the  major  premise  of  dilemmatic 
arguments  is  quite  clear.  For  if  the  dilemma  is 
thought  of  as  an  argument  which  leads  to  a  con- 
clusion through  the  affirmation  or  denial  of  alter- 
natives in  the  minor  premise,  the  major  premise  of 
such  an  argument  must  provide  the  basis  for  the 
alternatives  affirmed  or  denied  in  the  minor  premise, 
and  this  it  can  do  only  when  there  is  a  plurality  of 
terms  in  the  antecedent,  consequent,  or  both,  of 
the  major  premise.  In  view  of  these  more  general 
statements,  the  structure  of  the  dilemma  will  be 
evident  from  the  following  analysis : 

1.  The  major  premise  is  a  compound  hypothet- 
ical proposition 

a.  with  a  one-term  antecedent  and  a  two- 
term  consequent, 

with  a  two-term  antecedent  and  a  one- 
term  consequent,   • 

c.  or  with  a  two-term  antecedent  and  a  two- 
term  consequent. 

2.  The  minor  premise  is  a  disjunctive  proposi- 
tion, 


PROPOSITIONS  AND  ARGUMENTS  357 

3.     The  conclusion  is 

a.  either  a  categorical  proposition,  when  the 
major  premise  has  a  one-term  antecedent 
or  consequent. 

b.  or  a   disjunctive  proposition,   when   the 
major  premise  has  a  two-term  antecedent 
and  consequent. 

Classes  of  Dilemma.  Dilemmas,  which  are  gov- 
erned by  the  laws  of  the  hypothetical  syllogism,  are 
of  two  kinds,  —  Cojosiructive  and  Destructive.  ^A 
dilemma  is  said  to  be  constructive  when  the  minor 
premise  affirms  the  antecedent  of  the  major,  and  to 
be  destructive  when  it  denies  the  consequent  of  the 
major  disjunctively.  Within  each  of  these  kinds, 
there  are  two  forms,  —  Simple  and  Complex.  A 
dilemma  is  said  to  be  simple  when  its  major  premise 
has  a  single  antecedent  or  consequent,  and  it  is  said 
to  be  complex  when  both  the  antecedent  and  conse- 
quent of  the  major  premise  contain  two  terms.  We 
proceed  now  to  the  study  of  each  of  these  kinds  of 
dilemma,  and  to  an  examination  of  the  forms  that 
they  may  assume. 

i.  Constructive  Dilemma, — an  argument  which 
proceeds  from  the  acceptance  of  the  antecedent  to 
the  acceptance  of  the  consequent  of  the  major 
premise. 

(i)  Simple  Constructive  Dilemma, — an  argument 
whose  minor  premise  affirms  disjunctively  the  ante- 
cedent of  the  major,  and  whose  conclusion  categor- 
ically affirms  the  consequent. 


358  A  TEXT-BOOK   OF  LOGIC 

If  either  A  or  B,  then  C.,  If  a  science  furnishes  use- 
ful facts,  or  if  the  study  of  it  exer- 
cises the  reasoning  powers,  it  is 
worthy  of  being  cultivated; 

Either  A  or  B.  But  either  a  science  furnishes  useful 
facts,  or  its  study  exercises  the  rea- 
soning powers; 

Therefore,  C.  Therefore,  it  is  worthy  of  being  cul- 
tivated. 

(2)  Complex  Constructive  Dilemma, — an  a  r  g  u- 
ment  whose  minor  premise  disjunctively  affirms  the 
antecedent,  and  whose  conclusion  disjunctively 
affirms  the  consequent. 

If  A  then  C,  and  if  B  then  D.  If  Aeschines  joined 
in  the  public  rejoicings,  he  is  incon- 
sistent; if  he  did  not  he  is  unpa- 
triotic ; 

Either  A  or  B.    But  either  he  did  or  did  not; 
Therefore,  either  C  or  D.     Therefore,  he  is  either 

inconsistent  or  unpatriotic. 

2.  Destructive  Dilemma, — an  argument  which 
proceeds  from  the  denial  of  the  consequent  to  the 
denial  of  the  antecedent. 

(i)  Simple  Destructive  Dilemma, — an  argument 
whose  minor  premise  denies  disjunctively  the  conse- 
quent of  the  major,  and  whose  conclusion  categor- 
ically denies  the  antecedent. 

If  A,  then  both  B  and  C.  If  table-rappers  are  to  be 
trusted,  the  departed  are  spirits,  and 
they  also  exert  mechanical  energy ; 


PROPOSITIONS  AND  ARGUMENTS  359 

Either  not  B  or  not  C.  But  either  the  departed  are 
not  spirits  or  they  do  not  exert  me- 
chanical energy; 

Therefore,  not  A.  Therefore,  table-rappers  are  not 
to  be  trusted. 

(2)    Complex  Destructive  Dilemma, — a  n     a  r  g  u- 
ment  whose  minor  premise  disjunctively  denies  the 
consequent  of  the  major,  and  whose  conclusion  dis- 
junctively denies  the  antecedent. 
If  A  then  C,  and  if  B  then  D.    If  the  industry  of  the 
United  States  is  well  organised,  there 
is  work  for  every  efficient  labourer 
who  seeks  it,  and  if  all  labourers  are 
industrious,  they  will  seek  work. 
Either  not  C  or  not  D.    But  either  some  labourers 
cannot  get  work,   or  they   will   not 
seek  it; 

Therefore,  either  not  A  or  not  B.  Therefore,  either 
the  industry  of  the  United  States  is 
not  well  organised,  or  some  labourers 
are  not  industrious. 

The  Validity  of  the  Dilemma.  The  logical  value 
of  dilemmatic  arguments  has  frequently  been  called 
in  question.  Thus  Jevons  says,  "Dilemmatic  argu- 
ments are  more  often  fallacious  than  not."  It  may, 
therefore,  serve  to  emphasise  the  character  of  these 
arguments  if  we  indicate  where  their  use  may  in- 
volve us  in  error.  The  fallacious  character  of  a 
dilemma  must  be  sought  either  in  the  major  or  in 
the  minor  premise.  In  the  major  premise,  the  ante- 


860  A  TEXT-BOOK   OF  LOGIC 

cedent  or  consequent  may  not  express  possibilities, 
in  which  case  the  error  will  be  easily  detected;  or 
the  asserted  connection  between  them  may  be  false, 
in  which  case  the  error  is  likely  to  be  obvious.  For 
example,  if  we  do  not  admit  that  'A  is  B'  and  'A  is  C' 
are  possibilities,  then  we  are  not  likely  to  admit  that 
'If  A  is  B,  it  is  C'  is  a  possible  premise  of  an  argu- 
ment. But  if  we  admit  both  as  possibilities,  we  may 
not  admit  that  the  one  follows  as  a  consequence  from 
the  other,  and  this  will  preclude  'If  A  is  B,  it  is  C' 
from  figuring  as  the  major  premise  of  an  argument. 
We  thus  see  that  before  we  can  accept  a  compound 
hypothetical  proposition  as  the  major  premise  of  a 
syllogism,  we  are  required  to  admit  that  both  ante- 
cedent and  consequence  are  possibilities,  and  that 
they  are  related  to  each  other  as  condition  and  con- 
ditioned. For  example,  it  is  possible  for  a  triangle 
to  be  equilateral,  it  is  also  possible  for  a  triangle  to 
be  equiangular,  but  in  this  case  wherever  one  of 
these  possibilities  is  realised  the  other  is  also  found, 
the  one  is  conditioned  by  the  other.  These  are  the 
facts  that  we  express  in  the  statement,  'If  a  triangle 
is  equilateral,  it  is  equiangular/ 

Error  arises  most  frequently,  however,  in  the 
minor  premise.  The  reason  for  this  is  that  the 
alternatives  may  not  be  either  exhaustive  or  ex- 
clusive. The  difficulty  of  getting  a  dichotomous 
alternative  which  is  exhaustive  is  due  partly  to  the 
complex  nature  of  the  subjects  of  discourse,  and 
partly  to  the  fact  that  the  major  premise  of  these 
arguments  is  concerned  only  with  the  relation  of 


PROPOSITIONS  AND  ARGUMENTS  361 

antecedents  and  consequence,  and  not  with  disjunc- 
tive relations.  The  proposition  'If  A  is  B,  it  is  C 
or  D'  means,  as  we  have  seen,  that  'A  is  B'  is  the 
condition  of  both  'A  is  C'  and  'A  is  D/  When, 
therefore,  we  affirm  these  two  disjunctively  in 
the  minor  premise  of  an  argument,  we  must  do  so 
on  other  grounds  than  that  they  are  antecedents  or 
consequent  of  a  compound  hypothetical  major  pre- 
mise. Hence,  to  quote  Jevons,  "if  we  were  to  argue 
that  'if  a  pupil  is  fond  of  learning,  he  needs  no 
stimulus,  and  that  if  he  dislikes  learning,  no  stimulus 
will  be  of  any  avail;  but  as  he _is_ either  fond  of 
learning  or  dislikes  it,  a  stimulus  is  either^  needless 
or  of  no  avail,'  we  evidently  assume  improperly  the 
disjunctive  minor  premise.  Fondness  and  dislike 
are  not  the  only  two  possible  alternatives,  for  there 
may  be  some  who  are  neither  fond  of  learning  nor 
dislike  it,  and  to  these  a  stimulus  in  the  shape  of 
rewards  may  be  desirable.  Almost  anything  can  be 
proved  if  we  are  allowed  to  pick  out  two  of  the 
possible  alternatives  which  are  in  our  favor,  and 
argue  from  these  alone." 

REFERENCES. 

H.  A.  Aikins,  The  Principles  of  Logic,  Ch.  XVII. 
B.  Bosanquet,  The  Essentials  of  Logic,  Lecture  VI. 
J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Ch.  XI. 
J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Part  I.,  Ch. 

XVI. 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Lesson  XIX. 
J.  N.  Keynes,  Formal  Logic,  2d  Edition,  Part  III.,  Chs.  VII., 

VIII. 


362  A  TEXT-BOOK  OF  LOGIC 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  VII. 

W.  Minto,  Logic,  Inductive  and  Deductive,  Book  I.,  Part  IV., 
Ch.  VII. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Ch.  XII. 

W.  J.  Taylor,  Elementary  Logic,  Ch.  XII. 

ADVANCED 

B.  Bosanquet,  Logic,  Chs.  VI.,  VIII. 

F.  H.  Bradley,  The  Principles  of  Logic,  Book  I.,  Chs.  II.,  IV. 
W.  R.  B.  Gibson,  The  Problem  of  Logic,  Chs.  XXX.,  XXXI., 

XXXII. 

H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Ch.  XV. 
H.  Lotze,  Logic,  Book  I.,  Ch.  II.,  B,  C. 
F.  C.  S.  Schiller,  Formal  Logic,  Ch.  XVII. 

C.  Sigwart,  Logic,  Vol.  I.,  Part  I.,  Ch.  VII. 
J.  Venn,  Empirical  Logic,  Ch.  X. 

J.  Welton,  A  Manual  of  Logic,  Vol.  L,  Book  IV.,  Ch.  V. 

QUESTIONS 

1.  What  kind  of  predication  underlies  the  disjunctive  prop- 
osition? 

2.  What  relation  has  disjunctive  assertion  to  the  universe 
of  discourse? 

3.  Discuss  the  question  whether  the  alternatives  of  a  log- 
ical disjunction  are  exclusive. 

4.  "The  alternatives  of  a  disjunctive  proposition  must  be 
exhaustive."     Explain. 

5.  What  are  the  characteristics  and  significance  of  a  dis- 
tinctive syllogism? 

6.  Discuss  and  illustrate  the  main  classes  of  disjunctive 
syllogism. 

7.  Why  do  we  distinguish  classes  of  disjunctive  argument? 

8.  What  are  the  functions  of  the  minor  premise  and  con- 
clusion of  a  disjunctive  syllogism? 

9.  In  what  Moods  may  a  disjunctive  syllogism  be  stated? 


PROPOSITIONS  AND  ARGUMENTS  363 

10.  How  will  your  interpretation  of  'A  is  either  B  or  C'  be 
affected,   if  the   alternatives   are   understood   to   be  ex- 
clusive, and  if  they  are  understood  to  be  not  necessarily 
exclusive? 

11.  Why   is   the   disjunctive   syllogism   in    Modus   Tollendo 
Ponens  valid  whichever  view  of  alternation  we  take? 

12.  Why  is  a  disjunctive  syllogism  in  Modus  Ponendo  Tol- 
lens  valid  only  if  we  give  an  exclusive  reading  of  the 
major  premise? 

13.  What  is  a  hypothetical  proposition? 

14.  Name  and  state  the  difference  between  the  main  classes 
of  hypothetical  proposition. 

15.  What  is  meant  by  saying  that  the  material  of  the  judg- 
ments which  are  expressed  in  hypothetical  propositions 
is  possible  not  actual? 

16.  "Hypothetical  propositions  state  the  connection  of  a  sup- 
position and  what  follows  from  it."     Explain. 

17.  Into  what  two  parts  may  a  hypothetical  proposition  be 
analysed? 

18.  What  are  the  characteristics  of  a  hypothetical  syllogism? 

19.  Why  does  the  denial  of  the  antecedents,  and  the  affir- 
mation of  the  consequents  of  the  major  premise  of  a 
hypothetical  syllogism  make  it  impossible  to  state  any 
valid  conclusion? 

20.  What  are  the  rules  of  valid  inference  for  hypothetical 
arguments? 

21.  In  what  Moods  may  a  hypothetical  argument  be  stated 
validly? 

22.  In  what  Mood  is  a  hypothetical  argument  constructive? 

23.  Describe  and   illustrate   the   Modus    Ponens,   and    state 
why  hypothetical  arguments  in  this  Mood  are  valid. 

24.  State  and  illustrate  the  different  forms  of  the  Modus 
Ponens. 

25.  In  what  Mood  is  a  hypothetical  argument  destructive? 

26.  Describe   and   illustrate  the   Modus   Tollens,   and   state 
why  hypothetical  arguments  in  this  Mood  are  valid. 


364  A  TEXT-BOOK   OF  LOGIC 

27.  State  and  illustrate  the  different  forms  of  the  Modus 
Tollens. 

28.  What  is  it  to  be  'on  the  horns  of  dilemma'? 

29.  How   do   dilemmas,   trilemmas   and   tetralemmas    differ 
from  one  another? 

30.  Define  a  dilemma. 

31.  What   are  the  various   theoretically   possible   forms   of 
dilemma? 

32.  What  is  a  constructive  dilemma? 

33.  Describe  and  illustrate  the  various  forms  of  constructive 
dilemma. 

34.  What  is  a  constructive  dilemma? 

35.  Describe  and  illustrate  the  various  forms  of  destructive 
dilemma. 

36.  What  must  we  admit  with  respect  to  the  major  premise 
of  a  dilemma  before  it  can  serve  as  the  basis  of  a  valid 
conclusion? 

37.  What  sources  of  possible  error  are  found  in  the  minor 
premise  of  a  dilemmatic  argument? 

EXERCISES. 

1.  Write  three  disjunctive  propositions  in  which  the  alter- 
natives are  exhaustive  and  exclusive. 

2.  Construct  on  the  basis  of  your  answer  to  the  previous 
question  three  arguments  in  Modus  Ponens. 

3.  Construct  three  disjunctive  syllogisms  in  Modus  Tollens. 

4.  Write  three  hypothetical  propositions,  only  one  of  which 
may  be  introduced  by  'if.' 

5.  State  the  nature  and  Mood  of  the  following  arguments, 
and  examine  their  validity: 

(1)  If  the  study  of  logic  furnishes  the  mind  with  a  mul- 
titude of  useful  facts,  like  other  sciences,  it  would 
deserve  to  be  cultivated ;  but  it  does  not  furnish  the 
mind  with  a  multitude  of  useful  facts;  therefore, 
it  does  not  deserve  cultivation. 


PROPOSITIONS  AND  ARGUMENTS  365 

(2)  Mars  must  have  warmth  sufficient  for  protoplasmis 
metabolism,  if  life  exists  there;  but  life  is  not  pos- 
sible there,  since  the  planet  has  not  sufficient 
warmth  for  the  purpose  named. 

6.     What  are  the  nature  and  validity  of  the  following  argu- 
ments : 

(1)  If  you  say  what  is  just,  men  will  hate  you;  and  if 
you   say  what  is  unjust,  the  gods  will  hate  you. 
you  must  say  one  or  the  other.      Therefore,  you 
you  will  in  either  case  be  hated. 

(2)  If  he  were  clever,  he  would  see  his  mistake;  and  if 
he  were  candid  he  would  acknowledge  it.  But  either 
he  does  not  see  his  mistake,  or  will  not  acknowl- 
edge it.     Therefore,  he  is  either  not  clever  or  not 
candid. 


CHAPTER  XIII 
INDUCTION  AND  METHODS  PRELIMINARY  TO  INDUCTION 

General  Statement  of  the  Problem.  In  the  fore- 
going chapters,  knowledge  was  said  to  have  two 
sides,  from  one  of  which  it  is  seen  to  be  almost 
wholly  identified  with  what  we  call  truth,  and  from 
the  other  it  appears  to  be  almost  wholly  concerned 
with  what  are  called  facts.  On  whichever  of  these 
two  sides  of  knowledge  we  may  chance  to  look,  we 
are  exposed  to  the  danger  of  neglecting  the  other, 
and  thus  of  forgetting  that  the  distinction  of  truth 
and  fact  is  only  relative.  If  we  say  that  the  dis- 
tinction is  one  that  concerns  the  contrast  that  is 
ordinarily  made  between  our  thoughts-about-objects 
(truth)  and  the  objects-thought-about  (facts),  it 
will  not  require  a  great  deal  of  analysis  to  show  that 
truth  and  fact  are  not  two  separate  things,  but  two 
ways  of  looking  at  the  same  thing;  and  conse- 
quently, that  if  we  try  to  separate  them,  in  order 
to  give  exclusive  existence  to  either,  we  can  get  rid 
of  the  one  only  by  losing  our  grasp  also  upon  the 
other.  Thoughts  without  things  are  empty,  and 
things  without  thoughts  are  meaningless. 

Our  previous  discussions  have  led  us  to  lay  em- 
phasis mainly  upon  the  various  ways  in  which  our 
thoughts-about-things  are  capable  of  constant  im- 
provement and  expansion.  We  may  be  said  to  have 
taken  for  granted  the  existence  of  truth,  and  our 

(366) 


INDUCTION  AND   METHODS  367 

problem  was  to  study  the  methods  by  which  one 
truth  is  or  may  be  connected  with  another;  to  ex- 
pound in  an  elementary  way  the  systematic  char- 
acter of  truth.  From  this  point  of  view,  the  syllo- 
gism appeared  as  an  instrument  for  bringing  par- 
ticular truths  under  general  rules;  it  enabled  us  to 
see  what  were  the  conditions  of  the  connection  of 
one  truth  with  another.  In  definition  and  classifi- 
cation we  were  studying  how  to  make  truth  more 
explicit,  to  rid  it  of  ambiguity,  and  to  bring  out 
other  important  features.  In  brief,  we  have  been 
studying  the  judgment  as  the-  distinctive  element 
in  knowledge,  and  expounding  the  relations  that 
judgments  may  sustain  to  each  other. 

In  the  present  chapter,  we  turn  to  another  group 
of  problems  that  is  suggested  when  attention  is 
given  to  facts  rather  than,  truths.  Now  about 
facts,  the  logical  consideration  of  which  is  commonly 
referred  to  as  induction,  we  are  primarily  interested 
to  know  how  facts  are  constituted;  what  we  mean 
by  fact,  and  what  conditions  fact  must  satisfy  if 
the  world  of  fact,  like  the  world  of  truth,  is  to  be- 
come systematic.  Broadly  stated,  the  problem  of 
induction  is  an  inquiry  into  the  process  by  which, 
when  we  start  with  particular  facts,  universally 
valid  statements  about  reality  can  be  established. 

What  is  Meant  by  Fact.  There  are  several  fea- 
tures of  this  statement  of  the  problem  of  induction 
that  need  elucidation.  And  first,  what  precisely  do 
we  mean  by  fact?  The  word  is  used  in  a  narrower 
and  a  broader  way.  It  is  used  in  a  narrow  sense 


368  A  TEXT-BOOK  OF   LOGIC 

to  indicate  the  objects  of  our  knowledge  of  the  mate- 
rial world,  such  as  trees,  mountains,  railroads, 
streets,  houses,  etc.  In  the  broader  sense,  it  is  used 
to  indicate  any  object  of  knowledge,  whether  mate- 
rial or  not,  of  which  we  may  be  said  to  have  knowl- 
edge. Used  in  this  latter  way,  a  sensation,  an  idea, 
a  purpose,  an  emotion,  when  they  are  made  the 
objects  of  knowledge,  would  also  be  facts.  If  we 
compare  these  two  uses  of  the  word,  we  shall  see 
that  a  single  meaning  underlies  both;  they  differ 
only  in  the  range  of  its  application.  For  both,  a 
fact  is  any  object  of  which  we  are  said  to  possess 
knowledge. 

We  may  observe  further  that  by  knowledge  as  a 
conscious  process  is  meant  a  judging  process ;  hence, 
we  may  say  that  whatever  is  the  object  of  a  judging 
process  is  a  fact,  and  nothing  else  is.  What  a  judg- 
ing process  is  has  been  explained  in  earlier  chapters, 
and  it  is  important  here  merely  to  remark  that 
it  is  only  when  objects  are  made  the  subjects  of 
judgments,  and  are  qualified  in  distinctive  ways, 
that  they  can  be  spoken  of  as  facts.  Facts,  then, 
are  objects  that  have  been  qualified  by  our  thoughts 
about  them.  Now  there  are  a  number  of  ways  in 
which  facts  are  qualified  by  our  thoughts  about 
them ;  for  instance,  we  think  about  them  as  possess- 
ing certain  qualities,  as  being  in  a  certain  place,  as 
continuing  to  exist  for  a  certain  length  of  time,  as 
related  to  other  objects  in  numerous  ways.  The 
important  words  in  these  instances  are  quality, 


INDUCTION   AND   METHODS  369 

place,  time,  relation.    In  logic  these  are  called  cate- 
gories. 

The  problem  of  the  categories  is  much  too  diffi- 
cult a  subject  for  discussion  in  an  elementary  book 
of  logic,  but  the  student  is  required  to  understand 
at  least  what  the  word  means  and  how  it  is  used. 
We  may  say,  then,  that  the  categories  are  names 
for  the  differences  in  the  forms  of  our  thought  about 
things;  and,  because  thoughts  and  things  imply 
each  other,  they  indicate  also  a  distinction  in  the 
nature  of  the  things  about  which  we  think.  If  we 
remember  that  etymologically  category  means  pred- 
icate, the  categories  may  be  looked  upon  as  a  list  of 
the  classes  of  attributes  that  can  be  predicated  of  a 
subject  in  a  logical  proposition.  Thus,  if  we  say 
that  'Man  is  an  animal,'  the  term  animal  tells  us 
what  kind  of  a  substance  man  is;  we  are  thinking 
about  man  under  the  category  of  substance.  If, 
again,  we  say  that  The  violets  have  a  sweet  odour/ 
we  are  thinking  about  violets  under  the  category  of 
quality.  How  many  categories  or  generic  differences 
in  the  forms  of  our  thought  about  things  there  are 
is  a  matter  that  does  not  concern  us  here;  the  list 
varies  with  different  writers,  but  Aristotle  names 
ten.  The  point  to  emphasise  is  that  the  predicates 
of  logical  propositions  can  be  classified  under  a 
number  of  main  heads  which  denote  the  general 
forms  of  our  thinking  about  things,  and  these  forms 
of  thought  are  called  categories.  Until  we  have 
thought  the  objects  of  consciousness  under  one  or 
24 


370  A   TEXT-BOOK   OF  LOGIC 

more  of  the  categories  in  an  act  of  judgment,  they 
are  not  properly  called  facts;  a  fact  is,  from  this 
point  of  view,  any  object  of  consciousness  which 
has  been  thought  under  one  or  more  of  the  cate- 
gories. 

Nature  of  Reality.  Our  statement  of  the  induc- 
tive problem  contains,  secondly,  the  word  reality.  It 
is,  we  said,  about  reality  that  we  seek  universally 
valid  judgments.  What  is  reality?  The  answer  to 
this  question,  like  that  of  the  categories,  is  too  diffi- 
cult for  an  elementary  discussion,  and  besides  the 
subject  itself  belongs  to  another  department  of  phil- 
osophy, namely,  to  metaphysics.  But  we  may  under- 
stand the  term  well  enough  for  our  present  pur- 
poses, if  we  utilise  the  results  of  our  examination 
of  the  meaning  of  fact.  Broadly  stated,  by  reality 
is  meant  the  'world  of  fact.'  What  such  a  phrase  as 
that  just  employed  is  ordinarily  understood  to 
emphasise  is  that  facts  are  not  isolated,  unrelated 
things ;  that  they  are,  on  the  contrary,  connected  in 
numerous  ways  with  other  facts.  This  is  a  matter 
of  our  ordinary  every  day  observation  and  expe- 
rience. We  put  our  hand  in  the  fire  and  it  is  burned. 
We  eat  too  much  or  eat  the  wrong  things,  and  our 
bodies  suffer.  In  the  social  world,  we  have  a  dis- 
agreement with  one  person,  and  the  behaviour  of  a 
number  of  others  toward  us  is  affected  thereby. 
The  movements  of  the  planetary  bodies  regulate  our 
seasons,  the  rain  fall  determines  the  size  of  our 
crops.  These  instances  are  sufficient  to  suggest, 
what  is  true  throughout  our  experience,  that  facts 


INDUCTION   AND    METHODS  371 

do  not  exist  apart  from  each  other,  but  are,  so  to 
speak,  bound  up  in  bundles  together.    Such  bundles 
or  groups  of  fact  we  speak  of  as  worlds  of  fact. 
If  we  carry  our  observation  further,  it  will  appear 
that  as  individual  facts  are  related  to  each  other  so 
these  bundles  of  facts  are  connected  in  numerous 
ways.     The   combinations   of  these  more  complex 
groups  we  may  also  call  worlds  of  fact.     Thus  we 
have  the  world  of  commerce,  the  world  of  conduct, 
the  world  of  religion,  the  world  of  science.    Within 
each  of  these  worlds,  the  facts,  although  diverse, 
are  generically  related,  —  they  are  facts  of  a  given 
kind.     Looked  at  in  one  way,  it  seems  as  if  these 
several  worlds  had  little  if  anything  in  common,  and 
that  there  were  consequently  a  pluralism  of  such 
worlds.     A  little  closer  study  has  convinced  some 
men,  however,  that  we  can  detect  a  likeness  between 
some  of  these  worlds  on  the  ground  that  they  are 
concerned  with  material  things,  and  that  a  likeness 
exists  between  still  others  on  the  ground  that  they 
are  concerned  with  mental  things.     If  this  is  true, 
the  many  worlds  are  reduced  to  two,  each  of  which 
is  very  complex,  and  between  which  there  is  said 
to  exist  no  similarity  at  all.    Whether  this  is  true 
or  not  we  need  not  discuss ;  it  is  a  question  that  be- 
longs to  the  philosopher,  and  there  does  not  seem  to 
be  any  general  agreement  about  it.     The  point  to 
emphasise  is  that  whether  there  be  one  or  many 
worlds  of  fact,  every  one  is  agreed  that  when  we 
speak  about  reality  we  are  speaking  about  those 
worlds   and   the   facts   therein    contained.     When, 


372  A  TEXT-BOOK  OF  LOGIC 

therefore,  we  say  that  the  problem  of  induction  is 
an  inquiry  into  the  processes  by  which,  starting 
with  particular  facts,  universally  valid  statements 
about  reality  can  be  established,  we  mean  that  we 
are  interested  in  finding  out  the  truth  about  these 
worlds,  what  are  the  relations  between  the  facts 
which  give  these  worlds  their  characteristic  fea- 
tures, and  make  them  the  permanent  realities  they 
appear  to  be. 

Our  study  of  this  problem  falls  into  two  parts. 
In  the  first  part,  we  shall  consider  a  number  of 
processes  preliminary  to  induction,  and  with  which 
induction  frequently  has  been  confused;  in  the  sec- 
ond part,  we  shall  expound  the  inductive  process 
strictly  so-called,  a  process,  however,  which  we  shall 
see  emerging  into  a  clearer  and  clearer  light  in  our 
exposition  of  the  first  part.  The  present  chapter  is 
devoted  to  the  former  task;  the  next  four  to  the 
latter. 

Induction  by  Simple  Enumeration.  A  prevalent 
notion  identifies  induction  with  an  examination  of 
a  number  of  instances  of  a  given  phenomenon. 
Whenever  we  are  comparing  a  number  of  particular 
facts  for  the  purpose  of  discovering  in  what  re- 
spects they  are  alike,  we  are  supposed,  by  those  who 
hold  this  view,  to  be  engaged  in  an  inductive  pro- 
cedure. In  agreement  with  this  supposition,  the  dis- 
tinction has  been  drawn  between  perfect  and  imper- 
fect induction.  In  the  case  of  perfect  induction,  we 
are  dealing  with  a  group  of  facts  all  the  members 
of  which  are  known.  Thus,  we  may  make  state- 


INDUCTION  AND   METHODS  373 

ments  about  the  days  of  the  week  or  the  months  of 
the  year,  and  be  quite  sure  that  no  instances,  other 
than  those  we  have  examined,  will  occur  to  make  a 
revision  of  our  judgment  necessary.  We  may  say, 
for  example,  that  'All  the  months  of  the  year  have 
less  than  thirty-two  days,'  and  'The  week  consists 
of  seven  days.'  Whenever  the  group  of  facts  we  are 
examining  is  known  to  be  limited,  we  may  collect 
all  the  instances  and  observe  each  before  making 
the  general  statement.  The  enrollment  of  students 
in  a  college  class  is  such  a  definitely  limited  group, 
and  about  it  we  may,  for  example,  make  the  state- 
ment that  'None  of  the  students  in  this  class  is  over 
six  feet  tall.'  Imperfect  induction  is  based  upon 
the  same  principle  of  counting  and  comparing  in- 
stances, but  we  have  no  assurance  that  all  the  cases 
that  have  been  examined  are  all  the  cases  that  exist, 
and,  therefore,  a  lower  degree  of  certainty  is  sup- 
posed to  belong  to  the  statements  that,  under  these 
circumstances,  we  are  able  to  make.  This  was  the 
view  of  induction  commonly  held  during  the  Middle 
Ages.  It  consists  in  stating  that  all  the  known  in- 
stances of  a  given  kind  possess  a  certain  attribute, 
and,  therefore,  that  all  instances  of  this  kind  will 
be  found  to  possess  the  same  attribute.  For  ex- 
ample, the  Negroes  of  Africa  for  centuries  had  seen 
no  human  beings  who  were  not  black;  they  would, 
therefore,  suppose  that  all  human  beings  were  black. 
For  many  centuries  each  and  every  crow  that  had 
been  observed  by  Europeans  was  black;  it  was, 
therefore,  supposed  that  all  crows  were  black.  In 


374  A  TEXT-BOOK  OF  LOGIC 

both  these  instances  the  induction  has  been  found 
to  be  erroneous.  The  fault  to  which  every  imperfect 
induction  is  liable  is  that  experience  is  likely  at  some 
time  to  prove  it  wrong. 

Both  of  these  kinds  of  induction  have  been  re- 
jected by  writers  in  the  modern  era,  and  especially 
by  Bacon  and  Mill.  Perfect  induction,  Mill  says,  is 
of  no  scientific  value ;  the  conclusion  is  only  a  state- 
ment in  a  different  form  of  the  premises.  The  con- 
clusion, in  other  words,  is  merely  an  enumerative 
judgment,  —  a  judgment  which  summarises  the 
data  and  does  not  lead  beyond  them.  In  induction 
proper,  we  are  said  to  go  beyond  what  is  con- 
tained in  our  data ;  we  proceed  from  the  known  par- 
ticulars to  the  unknown  universal,  from  what  is 
true  of  a  given  case  or  number  of  cases  to  what  is 
true  always  and  everywhere  of  all  cases  whatsoever. 
Jevons,  on  the  other  hand,  defends  perfect  induc- 
tion, and  in  doing  so  states  very  well  the  value  that 
we  may  attach  to  this  process.  He  says:  "If  Per- 
fect Induction  were  no  more  than  a  process  of  abbre- 
viation, it  is  yet  of  great  importance,  and  requires 
to  be  continually  used  in  science  and  common  life. 
Without  it  we  could  never  make  comprehensive 
statements,  but  should  be  obliged  to  enumerate 
every  particular.  .  .  .  The  fact  is,  that  the  power 
of  expressing  a  great  number  of  particular  facts  in 
a  very  brief  space  is  essential  to  the  progress  of 
science.  Just  as  the  whole  art  of  arithmetic  con- 
sists in  nothing  but  a  series  of  processes  for  abbre- 
viating addition  and  subtraction,  and  enabling  us  to 


INDUCTION  AND   METHODS  375 

deal  with  a  great  number  of  units  in  a  very  short 
time,  so  Perfect  Induction  is  absolutely  necessary 
to  enable  us  to  deal  with  a  great  number  of  par- 
ticular facts  in  a  very  brief  space." 

The  case  of  imperfect  induction  is  not  in  prin- 
ciple different.  Imperfect  induction,  says  Bacon, 
"proceeds  by  merely  citing  instances  and  is  a  child- 
ish affair  (res  puerilis) ,  and  being  without  any  cer- 
tain principle  of  inference  it  may  be  overthrown  by 
a  single  negative  instance."  By  a  negative  instance, 
Bacon  means  an  instance  which  contradicts  all  the 
instances  that  previously  have  been  examined.  For 
example,  a  single  instance  of  a  grey  crow  over- 
throws the  inference  that  all  crows  are  black.  Mill, 
referring  to  imperfect  induction,  says  that  "it  con- 
sists in  ascribing  the  character  of  general  truths  to 
all  propositions  which  are  true  in  every  instance 
that  we  happen  to  know  of.  ...  In  science  it 
carries  us  but  a  little  way.  We  are  forced  to  begin 
with  it;  we  must  often  rely  on  it  provisionally,  in 
the  absence  of  means  of  more  searching  investiga- 
tion. But,  for  the  accurate  study  of  nature,  we  re- 
quire a  surer  and  a  more  potent  instrument."  This 
more  potent  instrument  is  "to  be  found  in  interro- 
gating nature"  by  experiment,  so  as  to  discover  the 
conditions  under  which  the  phenomena  occur. 

The  Value  of  Simple  Enumeration.  In  the  pre- 
ceding section,  we  have  examined  the  two  forms  of 
induction  by  simple  enumeration,  and  we  have  seen 
that  in  perfect  induction  all  the  positive  instances, 
and  in  imperfect  induction  a  larger  or  smaller  num- 


376  A  TEXT-BOOK  OF  LOGIC 

ber  of  the  positive  instances  of  a  phenomenon  are 
available  for  observation.  The  conclusion  that  is 
based  upon  a  complete  enumeration  of  the  instances 
does  not  go  beyond  these  instances  themselves, 
whereas  the  conclusion  that  is  based  upon  an  in- 
complete enumeration  is  understood  to  apply  also 
to  instances  that  have  not  been  examined  and  that 
may  not  be  known  to  exist.  In  the  former  case,  the 
conclusion  may  be  described  as  an  empirical  general- 
isation ;  in  the  latter,  the  conclusion  has  the  charac- 
ter of  an  hypothesis  which  is  held  subject  to  revision 
or  rejection  in  view  of  our  examination  of  other 
instances  that  may  come  to  light.  These  descrip- 
tions serve  to  distinguish  the  scientific  value  of  these 
two  forms  of  simple  enumeration.  Perfect  induc- 
tion belongs  to  the  stage  preliminary  to  induction, 
whilst  imperfect  induction  must  be  classed  among 
the  steps  of  induction  properly  so-called.  The  lat- 
ter, we  shall  reserve  for  future  consideration,  and 
turn  our  attention  immediately  to  the  former. 

Empirical  Generalisation.  Induction  by  complete 
enumeration,  which,  as  we  said,  leads  to  an  em- 
pirical generalisation,  is  not  entirely  a  simple  proc- 
ess, and  it  suggests  certain  questions  of  importance 
for  the  study  of  induction.  These  questions  we  shall 
consider  in  this  section.  And  first  we  should  ob- 
serve that  if  we  ask  why  there  is  any  such  process 
of  combining  in  single  statements  a  number  of  facts, 
why  we  classify  at  all,  we  may  perhaps  say  with 
Mill,  who  in  this  follows  Hume,  that  there  is  a  ten- 
dency of  the  mind  "to  generalise  its  experience,  pro- 


INDUCTION  AND   METHODS  377 

vided  this  points  all  in  one  direction."  This  abbre- 
viation and  summation  of  numerous  facts  and  expe- 
riences takes  place  as  a  measure  of  protection 
against  being  overwhelmed  with  the  diversity  of  the 
events  which  life  daily  presents  to  each  of  us.  It  is 
not  a  method  that  is  peculiar  to  science;  it  is  used 
by  all  of  us  in  common  life.  It  has  a  practical 
value;  it  does,  as  Mill  points  out,  facilitate  our 
handling  a  great  number  of  data.  But  because  we 
cannot  escape  using  it,  and  because  its  employment 
is  so  general,  the  method  is  not,  therefore,  altogether 
simple.  It  presupposes  the  existence  of  ideas,  —  of 
the  idea,  at  any  rate,  that  all  the  instances  we  ex- 
amine may  possibly  constitute  a  single  class.  When, 
however,  we  ask  by  virtue  of  what  particular  idea 
a  number  of  facts  constitute  a  class,  we  must  re- 
member that  classes,  as  we  saw  in  the  chapter  on 
classification,  are  not  ready  made  things ;  there  are, 
as  we  said,  no  'natural  kinds/  nor,  on  the  other 
hand,  are  there  any  ready  made  ideas,  except  as 
those  have  been  acquired  in  the  course  of  experience, 
that  can  serve  as  principles  of  classification.  The 
fact  is  that  we  classify  on  the  basis  of  observed  like- 
nesses, and  the  members  of  a  class  are  determined 
by  the  kind  of  likenesses  with  respect  to  which 
each  instance  is  examined.  In  science,  the  principle 
of  classification  is  consciously  entertained;  in  com- 
mon life,  it  is  not  brought  into  clear  definition.  In 
the  latter  case,  we  are  guided  by  the  accidental  at- 
tributes of  phenomena,  and  our  generalisations 
have,  as  a  rule,  the  value  merely  of  shorthand  mem- 


378  A  TEXT-BOOK   OF  LOGIC 

oranda ;  by  them  we  are  able  to  get  back  to  the  facts 
at  any  time  we  wish,  but  our  understanding  of  the 
facts  is  not  thereby  advanced.  The  process  is  not 
for  this  reason  without  value,  but  its  particular 
worth  is  likely  to  be  obscured  if  we  fail  to  observe 
its  limitations.  We  may,  therefore,  repeat  that 
empirical  generalisations  do  not  make  any  group  of 
facts,  for  science  or  for  common  life,  more  intel- 
ligible; they  merely  group  together  a  number  of 
data,  and  thereby  suggest  that  the  observed  mate- 
rial may  be  connected  in  some  more  fundamental 
way.  It  is  because  they  hint  at  some  underlying 
principle  of  connection  that  empirical  generalisa- 
tions have  a  place  in  the  method  of  scientific  inves- 
tigation. 

Colligation  of  Facts.  A  method  of  dealing  with 
facts  which  emphasises  more  directly  the  impor- 
tance of  ideas  in  the  development  of  knowledge  is 
that  which  is  called  by  Whewell  the  "colligation  of 
facts  by  means  of  an  exact  and  appropriate  concep- 
tion." Whewell  states  his  view,  and  defends  it 
against  the  objections  of  Mill,  by  calling  attention 
to  the  presence  of  ideas  in  all  our  perceptions.  He 
says,  "All  perception  of  external  objects  and  occur- 
rences involves  an  active  as  well  as  passive  process 
of  mind ;  —  includes  not  only  Sensations,  but  also 
Ideas  by  which  Sensations  are  bound  together,  and 
have  a  unity  given  to  them.  From  this  it  follows, 
that  there  is  a  difficulty  in  separating  in  our  per- 
ceptions what  we  receive  from  without,  and  what 
we  ourselves  contribute  from  within."  He,  there- 


INDUCTION  AND   METHODS  379 

fore  holds  that,  "we  cannot  obtain  a  sure  basis 
of  Facts,  by  rejecting  all  inferences  and  judgments 
of  our  own,  for  such  inferences  and  judgments  form 
an  unavoidable  element  in  all  Facts.  .  .  .  We 
are  not  able,  nor  need  we  endeavour,  to  exclude 
Ideas  from  our  Facts;  but  we  may  be  able  to  dis- 
cern, with  perfect  distinctness,  the  Ideas  which 
we  include."  In  agreement  with  this  position, 
what  Whewell  means  by  colligation  is  quite  clear; 
it  consists  in  bringing  together  a  number  of  ob- 
served facts  under  a  common  description,  as,  to 
use  one  of  his  own  illustrations,  when  Kepler,  hav- 
ing made  a  number  of  observations  on  the  suc- 
cessive positions  of  Mars,  brought  them  together 
under  the  one  conception  of  an  ellipse.  Mill  con- 
tends that  the  method  of  colligation  does  not  differ 
from  an  empirical  generalisation,  and  since  it 
involves  no  inference,  it  is  not  an  induction.  We 
do  not  need  to  go  into  the  dispute  between  Whewell 
and  Mill  on  these  points ;  it  is  clear,  from  the  state- 
ments of  what  colligation  means  for  Whewell,  that 
ideas  are  essential  to  the  existence  of  facts,  and  that 
a  conception  of  the  mind  operates  as  a  principle  of 
connection  between  facts.  The  relation  between 
fact  and  idea,  however,  is  not  always  stated  clearly 
by  Whewell,  for  he  sometimes  speaks  as  if  the  in- 
ductive act  consisted  of  a  superinduction  of  concep- 
tions upon  facts,  that  is,  as  if  facts  and  ideas  were 
external  to  each  other.  Green,  in  making  the  same 
point,  says  that  "Whewell  .  .  .  spoils  his  own 
case  (against  Mill)  by  often  writing  as  if  the  antith- 


380  A  TEXT-BOOK  OF  LOGIC 

esis  between  ideas  and  facts  were  a  valid  one;  as 
if  the  'superinduction  of  ideas'  upon  facts  were 
merely  an  operation  that  had  to  be  performed  ex 
parte  nostra  in  order  to  give  science."  The  value 
of  WhewelPs  insistence  upon  colligation  lies  in  this : 
it  asserts  that  all  our  knowledge  of  the  world  of 
fact  depends  upon  a  more  or  less  conscious  exercise 
of  the  judging  activity  which  carries  us  beyond  a 
merely  empirical  generalisation,  and  enables  us  to 
regard  the  facts  of  observation  under  a  new  point 
of  view.  These  points  of  view,  our  author  contends, 
are  supplied  by,  but  are  not  necessarily  derived 
from,  the  mind  itself.  As  we  shall  see  later,  the 
point  of  view  under  which  a  group  of  facts  becomes 
intelligible  is  sometimes  ascertained  by  a  stroke  of 
genius,  sometimes  as  the  result  of  a  laborious  and 
diligent  search.  But  however  it  may  have  been  dis- 
covered, ideas  and  the  facts  that  they  make  intelli- 
gible are  not  two  discrete  and  mutually  exclusive 
things;  they  are,  as  we  have  seen,  only  the  reverse 
sides  of  a  single  experience.  It  is  only  by  an  act 
of  analysis,  as  Whewell  himself  believes,  that  they 
can  be  distinguished. 

Parity  of  Reasoning.  We  often  entertain  beliefs 
about  new  facts  on  the  ground  of  the  similarity  of 
these  facts  to  other  facts  with  which  we  are  ac- 
quainted. For  instance,  if  the  bull  dogs  that  we 
have  known  are  unfriendly  toward  strangers,  we 
shall  shape  our  conduct  toward  any  dog  that  has 
the  general  appearance  of  this  breed  in  accordance 
with  the  belief  that  no  bull  dog  likes  strangers. 


INDUCTION  AND   METHODS  381 

This  is  an  example  of  an  empirical  generalisation. 
From  it  may  be  distinguished  another  type  of  rea- 
soning which,  while  dealing  with  numbers  of  in- 
stances, affirms  that  we  may  entertain  a  belief  about 
new  facts,  not  because  we  have  reason  to  entertain 
it  about  similar  facts,  but  because  we  may  apply 
to  the  new  facts  tests  similar  to  those  that  were 
used  on  the  old.  That  is,  if  we  have  shown  that  X 
is  true  of  A,  we  may  argue  that  it  is  true  also  of  B, 
not  because  it  is  true  of  A,  but  for  the  same  reason 
that  it  is  true  of  A.  This  method  of  argument  is 
called  parity  of  reasoning.  Mill's  illustration  is 
this:  "Having  shown  that  the  three  angles  of  the 
triangle  ABC  are  together  equal  to  two  right  angles, 
we  conclude  that  this  is  true  of  every  other  triangle, 
not  because  it  is  true  of  ABC,  but  for  the  same  rea- 
son which  proved  it  to  be  true  of  ABC."  Mill  objects 
to  calling  this  an  induction  on  the  ground  that  it 
"is  not  believed  on  the  evidence  of  particular  in- 
stances," that  is,  it  is  not  proved  in  each  of  the  in- 
stances, and,  therefore,  there  exists  no  ground  of 
inference  from  the  known  to  the  unknown  cases. 
The  importance  of  this  type  of  reasoning  at  our 
present  stage  of  inquiry  is  that  it  raises  definitely 
the  question  whether  numbers  of  instances  are 
necessary  for  an  inductive  conclusion. 

REFERENCES. 

H.  A.  Aikins,  The  Principles  of  Logic,  Ch.  XXIV. 

B.  Bosanquet,  The  Essentials  of  Logic,  Lecture  XI.,  a-d. 

J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Ch.  XIII. 


382  A  TEXT-BOOK  OF  LOGIC 

J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Part  II.,  Chs. 
II.,  III.,  a,b. 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Lessons  XXIV., 
XXV. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  VIII.,  §§  1,  2. 

W,  Minto,  Logic,  Inductive  and  Deductive,  Book  II.,  Chs.  I,  II. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Ch.  XV., 
§§  1-4. 

ADVANCED 

B.  Bosanquet,  Logic,  Vol.  II.,  Book  II.,  Chs.  II.,  V,  §§  3,  4. 
F.  H.  Bradley,  The  Principles  of  Logic,  Book  II.,  Part  II., 

Ch.  II. 
W.    R.    B.    Gibson,    The   Problem   of   Logic,    Chs.   XXXVII., 

XXXIX.,  XL.,  XLI. 
H.   W.   B.   Joseph,   An   Introduction   to   Logic,    Chs.   XVIII., 

XXIV. 

H.  Lotze,  Logic,  Vol.  II.,  Book  II.,  Ch.  VII. 
J.  S.  Mill,  A  System  of  Logic,  Book  III.,  Chs.  I.,  II.,  III. 
F.  C.  S.  Schiller,  Formal  Logic,  Ch.  XVIII. 
J.  Venn,  Empirical  Logic,  Ch.  XIV.,  XXIV. 
J.  Welton,  A  Manual  of  Logic,  Vol.  II.,  Book  V.,  Chs.  II., 

§  146,  III.,  §  148. 

QUESTIONS 

1.  What  do  you  assign  to  the  distinction  of  truth  and  fact? 

2.  In  what  two  ways  may  the  word  fact  be  used,  and  what 
common  element  is  present  in  both  uses? 

3.  'Facts    are    objects    that    have   been    qualified    by    our 
thoughts  about  them.'     Discuss. 

4.  What  is  a  category,  and  what  is  the  relation  of  cate- 
gories to  the  judgment? 

5.  What  is  a  fact  from  the  standpoint  of  the  categories? 

6.  What  is  meant  by  saying  that  reality  is  the  world  of 
fact? 


INDUCTION  AND  METHODS  383 


7.  What  light  does  the  study  of  the  worlds  of  fact  throw 
upon  the  problem  of  monism  and  pluralism? 

8.  How  must  we   interpret  the  inductive  problem,   if  by 
reality  is  meant  the  world  of  fact? 

9.  What  view  of  induction  is  implied  in  so-called  perfect 
and  imperfect  induction? 

10.  State  and  illustrate  what  is  meant  by  perfect  induction. 

11.  State  and  illustrate  what  is  meant  by  imperfect  induc- 
tion. 

12.  What  is  Mill's  criticism  of  perfect  induction? 

13.  What  is  Bacon's  estimate  of  imperfect  induction? 

14.  What  is  Bacon's  estimate  of  perfect  induction? 

15.  What,  according  to  Mill,  is  the  value  of  imperfect  in- 
duction? 

16.  What  is  the  value  of  perfect  and  imperfect  induction  as 
instances  of  simple  enumeration? 

17.  What  is  an  empirical  generalisation? 

18.  Why,  according  to  Mill,  do  we  generalise  our  experience? 

19.  'Generalisation  presupposes  the  existence  of  ideas.'    Ex- 
plain. 

20.  What    is    the    value    of    empirical    generalisation    for 
science  and  for  common  life? 

21.  State  WhewelFs  conception  and  explanation  of  the  col- 
ligation of  facts. 

22.  State  Mill's  objections  to  colligation. 

23.  What  is  Green's  criticism  of  Whewell's  position? 

24.  What  is  the  essential  truth  of  the  doctrine  of  colliga- 
tion? 

25.  What   is   parity  of  reasoning,   and   how  does   it   differ 
from  empirical  generalisation? 

26.  Why  does  Mill  refuse  to  regard  colligation  as  a  truly 
inductive  method? 

27.  What  is  the  importance  of  Mill's  objection? 


384  A  TEXT-BOOK  OF  LOGIC 


EXERCISES. 

1.  Give  at  least  six  examples  of  what  are  known  as  facts, 
and    distinguish    the    factual    and    truth    elements    in- 
volved in  these  examples. 

2.  Make  six  statements  of  fact,  and  determine  under  what 
category  each  statement  is  made. 

3.  Give  three  illustrations  of  what  is  known  as  reality  as 
distinguished  from  fact. 

4.  Give  three  illustrations  each  of  perfect  and  imperfect 
induction. 

5.  Write  out   two   examples   from   common   life   and   two 
from  science  of  an  empirical  generalisation. 

6.  Illustrate,  by  a  carefully  considered  example,  the  mean- 
ing of  a  colligation  of  facts. 

7.  Give  three  illustrations  of  parity  of  reasoning. 


CHAPTER  XIV 

SOME  DESCRIPTIVE   METHODS   OF   INDUCTION 

Relation  of  Numbers  of  Instances  to  an  Induction. 
The  question  with  which  we  closed  the  last  chapter, 
namely,  whether  numbers  of  instances  are  necessary 
for  an  induction,  may  be  made  the  starting  point 
of  the  present  one.  When  induction  is  thought  of 
as  an  inference  based  upon  the  examination  of  nu- 
merous instances  of  a  phenomenon,  it  assumes,  as 
we  have  seen,  two  forms :  one,  when  we  have  assur- 
ance that  all  the  instances  are  known;  the  other, 
when  no  such  assurance  can  possibly  be  entertained. 
The  former,  we  have  considered,  and  it  was  said  to 
be  an  illustration  of  a  method  of  organising  expe- 
rience that  is  not  confined  to  any  special  kinds  of 
fact,  but  is  used  over  the  whole  extent  of  our  life. 
The  name  that  we  gave  to  this  method  was  empirical 
generalisation.  The  value  of  empirical  generalisa- 
tions lies  in  the  fact  that  they  enable  us  to  deal 
with  large  numbers  of  data  in  a  simple  way;  we 
can  deal  with  collections  of  fact  as  single  facts 
whenever  we  ignore  the  differences  and  are  inter- 
ested in  the  likenesses  between  the  facts  which  enter 
into  such  collections.  The  assurance  that  every  one 
feels  in  organising  his  experience  in  this  manner  is 
due  to  the  limits  within  which  it  is  consciously  car- 
ried out.  Empirical  generalisations  are  held  to 
apply  only  to  the  instances  that  have  been  examined. 

25  (385) 


386  A  TEXT-BOOK   OF  LOGIC 

Numerous  instances  are  necessary  for  an  empirical 
generalisation,  but  such  generalisations,  since  they 
do  not  carry  us  beyond  the  instances  we  have  ex- 
amined, cannot  be  regarded  as  inductive  inferences. 

The  other  form  of  induction  by  simple  enumer- 
ation differs  from  the  one  just  considered  in  the  fact 
that  not  all  the  instances  of  the  phenomenon  have 
been  observed,  and  the  conclusion  which  the  known 
instances  are  found  to  warrant  is  extended  to  other 
instances  that  have  not  come  under  observation. 
The  question  we  are  concerned  with  in  such  a  case 
is  whether,  as  Mill  seems  to  hold,  the  validity  of  our 
inference  is  in  proportion  to  the  number  of  the  in- 
stances examined,  that  is,  whether  the  ground  of  the 
certainty  of  such  an  induction  is  found  in  the  num- 
ber of  the  instances  on  which  it  is  based ;  or  whether 
it  is  due  to  some  other  characteristic  of  the  in- 
stances, for  example,  to  the  nature  of  the  instances 
themselves. 

In  attempting  to  answer  this  question,  we  may 
observe,  in  the  first  place,  that  the  position  held  by 
Mill  emphasises  only  one  of  the  factors  of  an  enu- 
merative  induction,  and  that,  even  if  we  hold,  with 
him,  that  it  is  an  essential  factor,  it  nevertheless 
depends  for  its  effectiveness  on  the  co-operation 
of  another  factor  of  which  no  special  mention 
has  as  yet  been  made.  For  no  one  is  prepared 
to  maintain  that  the  mere  fact  of  numbers,  irre- 
spective of  the  other  qualities  of  the  instances  that 
an  induction  brings  under  review,  can  be  the  ground 
of  an  inference  to  other  unknown  instances.  Mill's 


SOME  DESCRIPTIVE    METHODS   OF   INDUCTION    387 

position,  therefore,  must  be  understood  to  be  that, 
although  a  greater  degree  of  certainty  attaches  to 
any  conclusion  we  reach  respecting  certain  observed 
facts  if  the  number  of  such  observed  facts  is  very 
great,  and  a  lower  degree  of  certainty  if  the  number 
of  such  observed  facts  is  relatively  few,  all  the  facts 
that  enter  into  an  induction  must  exhibit  the  qual- 
ities or  relations  with  respect  to  which  the  induction 
is  made;  and  that,  if  we  extend  to  other  instances 
the  conclusion  reached  with  respect  to  any  one 
group  of  instances,  this  is  possible  because  the  new 
instances  resemble  the  old  ones  in  their  essential 
nature.  Whether,  therefore,  we  are  interested  in 
arriving  at  an  induction  or  in  extending  to  new 
cases  the  conclusion  of  an  induction  already  made, 
the  fact  of  the  common  nature  of  all  the  instances 
must  be  established  or  assumed  if  the  induction 
itself  is  sound,  or  if  it  is  to  make  an  inference  pos- 
sible. In  either  case,  the  instances  in  question  must 
all  resemble  one  another  in  essential  respects. 

We  may  remark,  in  the  second  place,  that,  in  the 
light  of  what  has  now  been  shown,  the  question  of 
the  relation  of  numbers  of  instances  to  the  validity 
of  an  induction  is  an  interesting  rather  than  the 
most  important  aspect  of  the  inductive  problem. 
There  is  no  doubt,  for  example,  that,  within  limits, 
our  confidence  in  the  conclusion  of  an  induction  is 
increased  by  the  number  of  instances  by  which  it  is 
known  to  be  supported.  But  we  must  distinguish 
between  our  confidence  in  a  conclusion  and  the 


388  A  TEXT-BOOK  OF  LOGIC 

ground  on  which  the  truth  of  that  conclusion  is 
supposed  to  rest;  and,  we  must  remember,  it  is 
with  this  latter  question  that  we  are  here  concerned. 
But  we  may  say,  even  with  respect  to  our  confidence 
in  the  truth  of  inductive  conclusions,  that,  beyond 
certain  limits  which  vary  for  different  phenomena, 
this  is  not  affected  in  an  appreciable  manner  by  any 
considerable  increase  in  the  number  of  instances  of 
a  given  phenomenon  that  may  be  brought  to  our 
attention.  For  example,  should  we  not  feel  a  jus- 
tifiable impatience  with  any  one  who,  during  the 
hours  of  only  a  single  day,  counted  the  number  of 
objects  within  his  observation  that  fell  to  the 
ground,  and  who  informed  us  that  that  additional 
number  of  observed  cases  should  be  regarded  as  an 
additional  reason  for  our  confidence  in  the  law  of 
gravitation?  And  with  respect  to  the  truth  of  an 
inductive  process,  we  may  observe  that  the  number 
of  instances  that  need  to  be  observed  before  a  con- 
clusion is  reached  varies  according  to  the  nature  of 
the  instances  themselves,  and  the  ability  of  the  par- 
ticular individuals  who  examine  them.  If  this  is 
true,  the  number  of  instances  is  a  somewhat  un- 
certain factor  in  the  establishment  of  an  induction, 
and  there  seems  to  be  no  reason  why,  if  the  nature 
and  conditions  of  the  observation  are  sufficiently 
unambiguous,  the  truth  about  a  whole  class  of  cases 
may  not  be  reached  as  the  result  of  the  study  of  a 
single  example.  Indeed,  in  the  history  of  science 
there  have  been  instances  in  which  some  striking 
event  has  arrested  attention,  and  set  the  problem 


SOME  DESCRIPTIVE   METHODS   OF   INDUCTION    389 

for  the  scientist,  and  in  which  the  study  of  other 
examples  of  the  same  phenomenon  has  been  under- 
taken mainly  for  the  purpose  of  verifying  the  con- 
clusions reached  with  respect  to  the  single  instance. 
And,  further,  it  may  be  said  that,  whether  the  truth 
of  an  induction  has  been  reached  as  the  result  of 
an  examination  of  one  or  many  instances  of  a  phe- 
nomenon, we  may  infer  certain  facts  of  other  in- 
stances only  when  we  assume  that  these  also  re- 
semble the  old  one  or  ones  in  essential  respects.  In- 
deed, this  is  only  to  state  the  significance  that  be- 
longs to  all  scientific  statements  whatever,  and  it 
gives  the  reason  why  all  such  statements  are  essen- 
tially hypothetical.  Thus,  if  we  suppose  that  P  is 
a  phenomenon  under  examination,  and  that  X  is 
the  characteristic  with  respect  to  which  it  is  finally 
determined,  then  we  may  say  of  any  new  example 
M  that  'If  M  is  P,  it  is  X ;'  that  is  to  say,  X  is  pred- 
icated of  M,  because  it  is  P.  We  may,  therefore  con- 
clude, both  with  respect  to  the  establishment  of  an 
induction  and  with  respect  to  the  possibility  of  ex- 
tending an  induction  to  further  instances  of  a  phe- 
nomenon, that  "the  strength  of  an  induction  is  not 
proportional  to  the  number  of  instances  cited.  The 
generalisations  that  lead  to  the  most  trustworthy 
hypotheses  are  based,  not  on  the  counting  of  the 
number  of  instances,  but  on  the  weighing  of  their 
quality  and  character.  One  crucial  instance  may  be 
worth  a  hundred  others." 

Logical  Significance  of  Statistical  Methods.      The 
progress  of  modern  science  has  been  associated  so 


390  A  TEXT-BOOK  OF  LOGIC 

intimately  with  the  application  of  mathematical  con- 
ceptions to  concrete  phenomena  that  the  conclusion 
of  the  preceding  paragraph  may  appear  to  be  one- 
sided, if  not  erroneous.  To  meet  this  objection,  we 
shall  examine  the  logical  character  of  the  statistical 
methods,  and  ascertain  their  place  in  an  inductive 
process.  And,  at  the  outset,  we  should  observe  that 
whenever  statistical  methods  are  employed,  the  data 
under  observation  can  most  often  be  given  only  in 
the  form  of  aggregates  and  averages.  These  meth- 
ods, as  a  rule,  are  applied  distinctly  for  the  purpose 
of  ascertaining  the  numerical  distribution  of  cer- 
tain characteristics  which  have  come  under  obser- 
vation in  a  limited  number  of  cases.  Sometimes  all 
that  it  is  necessary  or  possible  to  do  is  to  ascertain 
the  total  number  of  the  recorded  instances  of  the 
phenomenon.  Usually,  however,  the  interests  we 
hope  to  satisfy  by  the  use  of  the  statistical  methods 
are  more  specialised  than  this.  For  instance,  we 
may  wish  to  know  what  is  the  average  occurrence 
of  some  irregular  group  character,  as,  for  example, 
the  average  number  of  insane  persons  born  per 
generation  in  a  particular  family.  Or  we  may  wish 
to  ascertain  the  average  amount  of  a  constant  group 
character,  as,  for  example,  the  average  amount  of 
butter  fat  given  per  head  by  a  particular  breed  of 
cattle.  And  even  when  these  methods  are  applied 
to  individuals,  we  still  have  in  view  the  discovery 
of  group  characteristics.  On  this  point  Thorndike 
writes:  "The  sciences  of  human  nature  commonly 
use  measures  of  individuals  only  in  order  to  get 


SOME  DESCRIPTIVE   METHODS  OF   INDUCTION   391 

measures  of  groups.  Not  John  Smith's  spelling 
ability,  but  that  of  all  fifth  grade  boys  taught  by  a 
certain  method;  not  A's  delicacy  of  discrimination 
of  weights,  but  that  of  all  men;  not  B's  wage,  but 
that  of  all  railroad  engineers  during  a  certain 
period ;  not  C's  children,  but  the  productivity  of  the 
English  race  as  a  whole ;  not  individuals,  but  groups, 
are  commonly  measured,  compared  and  argued 
about."  An  examination  of  the  individuals  enu- 
merated in  the  census  returns  as  to  age,  sex,  married, 
unmarried,  etc.,  also  illustrates  that  interest  in  the 
characteristics  of  groups  which  prompts  the  use  of 
distinctly  statistical  methods  of  inquiry.  Sociological 
and  insurance  tables,  as  well  as  those  of  the  phys- 
ical, biological  and  psychological  sciences,  are  based 
upon  the  same  interest.  The  particular  service, 
therefore,  that  the  employment  of  statistical  meth- 
ods is  able  to  render  is  to  bind  together  diverse 
numbers  of  fact  of  a  particular  kind,  and  thus  to 
provide  a  basis  for  the  comparison  of  otherwise 
incomparable  aggregates.  "The  method  of  count- 
ing .  .  .  agreements  and  comparing  results," 
says  Gibson,  "constitutes  the  Method  of  Statistics." 
The  conclusions  to  which  statistical  inquiries 
lead  are  generalisations,  but  they  are  to  be  distin- 
guished from  the  empirical  generalisations  spoken 
of  above  in  two  respects.  In  the  first  place,  statis- 
tical conclusions  may  be  taken  as  a  type  of  scientific 
as  contrasted  with  empirical  generalisation  on  the 
ground  that  they  are  the  products  of  a  systematic 
investigation  of  numbers  of  fact.  By  systematic  in 


392  A  TEXT-BOOK   OF  LOGIC 

this  connection  we  mean  that  the  basis  of  the  class- 
ification of  data  is  in  each  case  consciously  chosen, 
and  that  it  is  applied  as  a  test  of  what  can  and  what 
cannot  be  included  in  the  numeration.  For  example, 
in  an  enumeration  of  houses  in  India,  as  Scripture 
points  out,  great  difficulty  was  experienced  on 
account  of  the  indefiniteness  of  what  was  meant  by 
a  house.  Similarly,  the  Weather  Bureau  would  find 
it  impossible  to  classify  the  hot,  temperate,  and  cold 
days  during  a  single  year  because  of  the  indefinite- 
ness  of  the  connotation  of  these  terms.  But  if  hot 
is  defined  as  a  shade  temperature  above  75°,  cold 
as  a  shade  temperature  below  35°,  and  temperate 
any  degree  between  these  two,  it  is  readily  seen  that 
there  will  be  no  difficulty  in  applying  to  the  days 
of  the  year  these  tests,  and  generalising  the  results. 
In  the  second  place,  statistical  conclusions  are  ex- 
pressed always  in  quantitative  terms.  This  is,  of 
course,  not  an  accident;  it  is  a  result  directly  aimed 
at.  In  this  way,  certain  features  of  the  objects  of 
our  experience  come  to  have  a  value  and  significance 
which,  under  any  other  method  of  observation, 
would  be  in  danger  of  being  overlooked  altogether. 
For  example,  isolated  events,  and  events  that  occur 
but  rarely  in  our  experience,  unless  they  are  very 
striking,  are  liable  to  receive  but  a  passing  notice, 
and  to  present  but  a  small  part  of  their  meaning  to 
such  casual  observation.  It  is  also  true  that  we  are 
prone  to  overlook  the  import  of  those  occurrences 
which  are  brought  regularly  to  our  notice.  Famil- 
iarity breeds  neglect  as  surely  as  do  entire  novelty 


SOME  DESCRIPTIVE   METHODS   OF   INDUCTION    393 

and  strangeness.  The  average  person  seems  to 
dwell  in  safety  between  these  two  extremes,  with 
the  result  that  the  world  presents  him  with  few 
problems,  and  stimulates  him  but  rarely  to  sus- 
tained intellectual  effort.  It  is,  however,  a  charac- 
teristic of  the  scientific  mind  that  there  is  nothing 
so  common  that  it  does  not  deserve  comprehension, 
and  nothing  so  rare  that  it  is  beyond  consideration. 
Out  of  this  temper  have  been  born  those  efforts  to 
reduce  the  passing  show  of  our  daily  experience  to 
a  definite  system  and  order;  and  it  has  seemed,  to 
those  engaged  in  it,  not  the  leas£  worthy  task,  as  it 
has  been  not  the  least  profitable,  to  count  the  num- 
ber of  times  a  given  fact  occurs,  and  to  make  num- 
ber a  part  of  the  facts  themselves.  Among  the 
Greeks,  Pythagoras  interpreted  the  world  in  this 
mathematical  way ;  and  all  our  modern  sciences,  the 
physical,  biological  and  social,  are  employing  statis- 
tics in  the  belief  that  when  the  relative  frequency 
of  the  occurrences  of  a  phenomenon  is  known,  the 
phenomenon  itself  has  been  more  accurately  ob- 
served, and  can  be  more  exactly  described. 

Qualitative  Methods  of  Observation.  Statistics, 
however,  do  not  provide  the  only  methods  by  which 
the  observation  of  phenomena  is  carried  on.  There 
are  classes  of  phenomena  to  which  it  cannot  be 
fruitfully  applied.  We  have  said  that  whenever 
our  material  can  be  presented  most  advantageously 
in  the  form  of  aggregates  and  averages,  statistics 
lend  themselves  as  a  means  of  bringing  out  features 
of  this  material  that  in  no  other  way  receives  ade- 


394  A  TEXT-BOOK   OF  LOGIC 

quate  recognition.  But  we  are  not  always  or  only 
interested  in  collective  groups  of  objects.  We  are 
also  interested  in  objects  as  instances  of  a  genus,  as 
instances  in  which  the  characteristics  of  a  genus 
are  given  concrete  expression.  For  instance,  when- 
ever we  call  a  certain  flower  a  primrose,  we  are- not 
describing  the  flower  as  an  individual  thing;  rather 
are  we  neglecting  altogether  what  is  peculiar  to  the 
flower  as  an  individual,  what  makes  it  this  primrose 
rather  than  that ;  and  are  recounting  the  character- 
istics which  this  object  shares  with  an  indefinite 
number  of  other  specimens  of  the  same  species.  The 
difference  between  this  case  and  those  that  are 
amenable  to  statistical  observation  is  that  in  the 
latter  we  need  to  collect  together  numbers  of  indi- 
viduals before  the  important  characteristics  are 
open  to  observation,  whereas  in  the  former,  the  indi- 
vidual instance  displays  all  the  attributes  that  are 
distinctive  of  the  genus  to  which  it  belongs.  Field 
botany,  as  our  illustration  suggests,  is  a  descriptive 
science  in  the  sense  we  are  now  indicating.  Natural 
history  and  descriptive  geology  also  belong  to  the 
same  class.  In  these  sciences,  individual  objects  dis- 
play universal  characteristics,  that  is,  those  which 
in  our  experience  are  found  to  belong  to  an  indefi- 
nite number  of  other  objects  of  the  same  kind  or 
class.  These  common  features  of  objects  have  their 
interest,  and  they  set  for  us  problems  which  tax  our 
industry  and  challenge  our  efforts  to  solve.  It  is 
obvious,  in  the  light  of  these  statements,  that  the 
accurate  knowledge  which  is  the  goal  of  our  intel- 


SOME  DESCRIPTIVE    METHODS   OF   INDUCTION    395 

lectual  life  is  not  all  of  a  single  type,  and  that  the 
methods  of  observation  which  we  adopt  or  devise 
must  be  appropriate  to  the  nature  of  the  objects 
which  are  the  material  of  our  study.  Sometimes 
we  must  avail  ourselves  of  the  quantitative  methods 
of  statistical  observation,  sometimes  of  the  quali- 
tative methods  of  immediate  perception. 

The  Nature  of  Scientific  Observation.  Whatever 
the  methods  of  observation  may  be,  and  however 
numerous,  they  are  determined  by  the  nature  and 
purpose  of  observation  itself.  Now,  in  order  to  gain 
a  clear  understanding  of  the  nature  and  purpose  of 
observation,  we  may  distinguish  scientific  observa- 
tion from  the  attitude  we  are  accustomed  to  main- 
tain toward  the  ordinary  events  and  circumstances 
of  our  every  day  life.  Those  adjustments  with  our 
environments  which,  during  the  course  of  our  early 
years,  we  have  succeeded  in  acquiring  have  been 
determined  almost  exclusively  by  practical  consider- 
ations, and  they  have  been  maintained  as  the  habits 
of  our  lives  very  largely  on  account  of  their  value 
as  instruments  of  physical  and  social  survival.  The 
earliest  task  that  devolves  upon  the  infant  is  to 
come  into  relations  with  the  world  around  him,  and 
his  primary  concern  is  with  the  world  of  material 
things  from  which  he  may  receive  either  benefit  or 
harm.  It  is  only  so  far  as  it  contributes  to  this  end 
that,  in  its  earliest  beginning,  the  mind  of  the  child 
is  stimulated  into  activity,  and  his  interest  is 
aroused  in  the  things  and  persons  which  constitute 
his  world.  Intelligence,  that  is  to  say,  is  a  later 


396  A   TEXT-BOOK   OP  LOGIC 

development  than  are  those  motor  responses  to 
environment  through  which  the  well-being  of  the 
individual  is  secured,  and  comes  at  first  upon  the 
scene  of  the  individual's  life,  not  in  order  to  intro- 
duce any  new  interest  or  to  initiate  a  new  set  of 
aims,  but  as  the  guide  and  servant  of  the  practical 
which,  through  its  means,  is  enlarged  and  rendered 
more  efficient.  These  relations  of  the  practical  and 
intellectual  in  the  order  of  their  development  throw 
an  interesting  light  upon  the  function  that  intelli- 
gence plays  in  the  maintenance  of  human  existence ; 
for,  as  it  was  in  the  beginning,  so  does  it  remain  for 
the  greater  part  of  each  individual's  life,  there 
is  no  independent  intellectual  interest,  and  the  func- 
tions of  human  understanding  are  determined 
throughout  by  the  practical  purpose  which  they 
instrumentally  advance.  If,  in  view  of  these  con- 
siderations, we  observe  the  characteristics  of  our 
ordinary  life,  we  shall  understand  why,  instead  of 
displaying  a  careful  attention  to  details,  the  per- 
ceptual consciousness  has  a  conspective  range  which 
enables  it  to  take  in  a  large  amount  of  detail  with- 
out losing  its  practical  effectiveness.  What  is  not 
of  practical  importance  fails  to  be  noticed;  only 
those  features  of  the  environment  which  are  prac- 
tically important  are  gathered  up  and  made  objects 
of  attention. 

How  far  perception,  as  it  is  ordinarily  employed, 
is  from  giving  accurate  knowledge  of  the  common- 
place facts  and  events  of  life  is  well  known.  As  an 


SOME  DESCRIPTIVE   METHODS   OF   INDUCTION    397 

example  of  the  unreliability  of  everyday  observa- 
tion, we  may  cite  the  contradictory  accounts  of  eye- 
witnesess  of  a  common  street  accident.  But,  fur- 
ther, the  conclusions  and  inferences  that  we  base  on 
such  observations  are,  as  a  rule,  no  more  trust- 
worthy than  the  observations  themselves.  In  our 
daily  life  we  exhibit  constantly,  what  Whewell  calls, 
"  a  vague  and  loose  mode  of  looking  at  facts/'  As 
a  result,  to  quote  from  the  author  just  referred  to, 
we  remain  "for  a  long  time  under  the  belief  that  a 
body,  ten  times  as  heavy  as  another,  falls  ten  times 
as  fast;  that  objects  immersed  in  water  are  always 
magnified,  without  regard  to  the  form  of  the  sur- 
face; that  the  magnet  exerts  an  irresistible  force; 
that  crystal  is  always  found  associated  with  ice; 
and  the  like.  These  and  many  others  are  examples 
of  how  blind  and  careless  men  can  be,  even  in  obser- 
vation of  the  plainest  and  commonest  appearances; 
and  they  show  that  the  mere  faculties  of  perception, 
although  constantly  exercised  upon  innumerable 
objects,  may  fail  in  leading  to  any  exact  knowl- 
edge." 

If  now  we  consider  what  may  properly  be  called 
scientific  observation,  we  shall  see  that  this  differs 
from  immediate  perception  in  important  respects. 
Scientific  observation,  in  the  first  place,  has  not  the 
conspective  range  of  immediate  perception,  but  is 
characterised  by  a  close  attention  to  detail  within  a 
limited  field.  This  difference  is  conditioned  by  the 
difference  in  the  purpose  for  which  each  exists. 
The  purpose  that  controls  the  character  and  direc- 


398  A  TEXT-BOOK   OF  LOGIC 

tion  of  our  perceptions  was  seen  to  have  its  origin 
in  the  interests  of  our  practical  life.  There  is  not, 
on  the  other  hand,  any  such  thing  as  observation  in 
the  strict  meaning  of  the  term,  until  our  interest  in 
the  world  of  the  practical  life  has  failed  to  be  satis- 
fied, either  because  the  environment  is  too  complex 
for  perception  to  cope  with,  or  because  the  relevant 
features  of  the  environment  have  been  hastily  over- 
looked. In  either  case,  importance  comes  to  be  at- 
tached to  the  details  of  a  situation,  and  the  condi- 
tions are  favourable  for  the  development  of  an  in- 
terest in  details  quite  apart  from  the  regulation  of 
our  ordinary  practical  activities.  Scientific  obser- 
vation does  not  differ  from  immediate  perception  in 
the  fact  that  the  former  is,  and  the  latter  is  not, 
purposive,  but  in  the  character  of  the  purpose  which 
prescribes  the  goal  and  directs  the  course  of  each. 
In  the  case  of  scientific  observation,  the  purpose 
that  renders  the  details  of  an  event  or  situation  im- 
portant is  theoretical;  it  springs  from  the  interest 
we  have  in  gaining  an  intimate  acquaintance  with 
these  situations  and  events.  That  is  to  say,  scien- 
tific observation  must  needs  be  used  when  we  are 
launched  upon  a  search  for  truth;  it  is  an  instru- 
ment of  our  acquisition  of  knowledge.  What  things 
are,  and  how  they  come  to  be  what  they  are,  are 
the  questions  which  emphasise  the  necessity  of  accu- 
rate observation. 

In  contrast  with  immediate  perception,  scientific 
observation  is,  in  the  second  place,  analytic ;  it  seeks 
in  the  environment  for  those  features  which  are 


SOME  DESCRIPTIVE   METHODS   OF   INDUCTION    399 

relevant  to  the  theoretical  purpose  by  which  it  is 
guided.  The  difficulty  that  one  experiences  in  his 
earliest  scientific  efforts  is  due  to  this  selective 
character  of  observation.  If,  for  example,  we  placed 
an  histological  preparation  under  the  microscope, 
and,  without  any  previous  acquaintance  with  the 
subject  to  which  it  relates,  we  were  to  attempt  to 
observe  the  character  of  the  tissue,  we  should  very 
likely  fail;  and  our  failure  would  be  due  probably 
to  the  fact  that  we  had  no  defined  purpose  to  guide 
our  selection  of  the  relevant  detail.  The  beginner 
in  any  science  is  subjected  to  much  loss  of  time  and 
unnecessary  discouragement  if  the  instructor  does 
not  understand  that  scientific  observation  does  not 
consist  in  looking  at  a  mass  of  detail,  but  in  looking 
for  certain  relevant  aspects  in  a  mass  of  detail.  But 
to  look  for  something  relevant  implies  that  a  pur- 
pose is  functioning  in  our  examination  of  objects, 
and  it  is  this  purpose  or  idea  which  the  capable 
instructor  provides  as  the  guide  to  his  pupil's  obser- 
vation. We  observe  only  what  we  are  prepared  to 
observe,  and  mere  collections  of  fact  are  useless 
until  an  idea  illuminates  and  makes  them  intel- 
ligible. This  view  of  scientific  observation  is  illus- 
trated in  the  work  of  all  the  great  scientists.  It 
was  conspicuously  true,  for  example,  of  Darwin, 
of  whom  his  son  writes :  "He  often  said  that  no  one 
could  be  a  good  observer  unless  he  was  an  active 
theoriser.  This  brings  me  back  to  what  I  said 
about  his  instinct  for  arresting  exceptions,  it  was 
as  though  he  were  charged  with  theorising  power 


400  A  TEXT-BOOK   OF  LOGIC 

ready  to  flow  into  any  channel  on  the  slightest  dis- 
turbance, so  that  no  fact,  however  small,  could  avoid 
releasing  a  stream  of  theory,  and  thus  the  fact  be- 
came magnified  into  importance."  In  other  words, 
we  observe  not  with  our  senses  but  with  our  intel- 
ligence. Or,  as  Huxley  put  it,  what  one  sees  when 
he  looks  through  a  microscope  depends  as  much 
upon  what  is  behind  the  eye-piece  as  upon  what  is 
under  the  objective. 

Experimental  Observation.  If  we  reduce  the  idea 
of  a  scientific  experiment  to  its  lowest  terms,  we 
may  say  that  it  consists  in  the  interposition  of  an 
instrument  of  precision  between  our  sense  organs 
and  the  material  we  are  studying.  From  this  point 
of  view,  a  scientific  experiment  secures  an  extension 
of  the  range  of  our  perceptive  organs,  and,  in  so  far 
as  it  does  this,  brings  out  more  of  the  detail  of  the 
material  under  examination.  The  balances  of  the 
physicist,  the  microscope  of  the  biologist,  the  tele- 
scope of  the  astronomer  are  devices  for  thus  extend- 
ing the  field  of  scientific  observation.  But  there  are 
limitations  to  experimental  observation,  as  thus 
understood,  which  often  would  hinder  the  progress 
of  truth  if  they  were  not  offset  by  observation  under 
normal  conditions.  Hence,  as  Lotze  says,  "Observa- 
tion often  acquaints  us  with  broad  characteristics 
of  phenomena,  which  in  experiment  would  have 
been  obscured  by  special  conditions."  The  fact  is 
that  observation  and  experiment  supplement  each 
other,  and  there  are  cases  when  neither  alone  could 
lead  us  as  far  as  when  both  are  used  in  conjunction. 


SOME  DESCRIPTIVE   METHODS  OF   INDUCTION,  401 

There  are  also  some  phenomena  to  which  experi- 
mental observation  cannot  be  applied  at  all,  and  for 
our  examination  of  these  we  must  rely  upon  other 
means  of  observation.  In  this  connection,  it  may  be 
recalled  that  Darwin's  great  work  was  achieved  by 
the  method  of  observation,  in  the  broad  sense  just 
described,  rather  than  by  the  methods  of  experi- 
mental observation. 

A  further  consideration  affecting  our  view  of 
the  range  of  scientific  observation  is  that,  however 
successful  we  may  be  in  improving  our  present 
apparatus,  and  in  devising  and  constructing  new 
apparatus,  there  is,  in  all  probability,  a  limit  beyond 
which  our  sense  organs  are  not  capable  of  being 
supplemented  in  that  way,  and  a  point,  consequently, 
at  which  the  observations  we  make  by  the  use  of 
instruments  of  precision  must  stop.  What  the 
scientist  does  when  he  has  reached  his  actual  per- 
ceptual limits,  and  what  he  would  attempt  to  do  if 
he  reached  the  theoretically  possible  limits  of  per- 
ception, is  to  supplement  his  actual  observations 
by  guesses  as  to  what,  if  perception  were  possible, 
further  observation  would,  in  all  probability,  make 
known.  In  some  such  way  as  this  have  the  lumin- 
iferous  ether,  atoms,  ions,  etc.,  become  parts  of  the 
actual  working  data  of  science,  data,  be  it  remarked, 
that  are  regarded,  by  science,  as  truly  material  sub- 
stances as  are  the  grosser  bodies  that  are  now  within 
the  range  of  present  perception.  This  kind  of  obser- 

2$ 


402  A  TEXT-BOOK  OF  LOGIC 

vation  we  may  call,  for  the  sake  of  convenience  of 
reference,  theorising,  or  theoretical  observation. 

Another  characteristic  of  experimental  observa- 
tion is  that,  like  all  observation,  it  must  be  used  in 
the  service  of  the  purpose  which  directs  the  obser- 
vation. Hence  the  impossibility  of  any  one  being 
an  experimental  scientist  who  is  not  thoroughly 
acquainted  with  the  mechanical  structure  of  the 
apparatus  which  he  either  uses  or  designs.  There 
is  a  quite  prevalent  notion,  especially  among  stu- 
dents and  inexperienced  instructors,  that  one  is 
necessarily  an  experimentalist  if  he  works  in  a 
laboratory  and  manipulates  apparatus.  To  these, 
no  question  could  come  with  more  pertinence  than 
this:  Tor  what  purpose  are  you  using  this  par- 
ticular piece  of  apparatus,  and  precisely  in  what 
way  does  it  enable  you  to  realise  this  purpose?'  It 
is  not  apparatus  that  lends  significance  to  our  ideas, 
but  ideas  that  make  our  apparatus  intelligible  in- 
struments of  observation.  To  lose  sight  of  this 
truth  is  to  miss  entirely  the  true  meaning  of  experi- 
mental science;  for  we  may  be  as  passively  assimil- 
ative when  looking  through  a  microscope  as  we 
might  be  actively  observant  when  using  our  natural 
organs  of  perception.  But  when  our  apparatus 
"passes  into  the  service  of  an  idea,  and  we  proceed 
to  put  our  object  under  such  conditions  as  the  idea 
requires  for  testing  and  verifying  itself,  our  obser- 
vation is  no  longer  merely  passive,  but  experi- 
mental. A  definite,  purposive  interference  of  some 
sort  with  the  production  of  the  phenomenon  to  be 


SOME  DESCRIPTIVE    METHODS   OF   INDUCTION    403 

noted  is  the  desideratum"  of  experimental  observa- 
tion. 

At  precisely  what  point  can  this  interference 
with  the  phenomenon  be  introduced  most  advanta- 
geously? The  answer  to  this  question  is  given 
unanimously  by  all  the  workers  in  the  field  of 
science.  Science  seeks  to  control,  not  the  nature, 
but  the  conditions  of  the  occurrence  of  phenomena. 
"To  observe  with  accuracy  and  convenience,"  says 
Jevons,  "we  must  have  agents  under  control,  so  as 
to  raise  or  lower  their  intensity,  to  stop  or  set  them 
in  action  at  will."  Welton  writes:  "Appeal  to  ex- 
periment is,  then,  necessary  whenever  simple  obser- 
vation alone  will  not  make  plain  all  the  essentials 
of  a  phenomenon;  and  its  object  is  to  eliminate  all 
the  conditions  which  are  not  specially  operative  in 
the  particular  case  under  observation."  In  like 
strain  Gibson  says:  "Control  over  the  conditions 
under  which  the  object  shall  present  itself  for  study 
is  the  great  desideratum  and  the  factor  in  experi- 
mental observation  which  most  influences  the  pre- 
cision and  certainty  of  the  results  obtained.  Such 
control  enables  us  to  vary  the  circumstances,  and  to 
repeat  the  observation  as  often  as  we  please  by 
simply  reproducing  the  concurrence  of  conditions 
requisite  for  bringing  into  play  the  desired  effect." 

REFERENCES 

SEE  THE  END  OF  THE  NEXT  CHAPTER 


404  A  TEXT-BOOK  OF  LOGIC 


QUESTIONS 

1.  What  are  nature,  extent  and  value  of  empirical  general- 
isations? 

2.  Does  an   empirical  generalisation  involve  an   inductive 
inference?    What  is  your  reason? 

3.  Are  numerous  instances  of  a  phenomenon  necessary  for 
an  empirical  generalisation?    Why? 

4.  Can  imperfect  induction  be  regarded  as  an  example  of 
an  inductive  inference?     State  reasons  for  your  answer. 

5.  What   problem   is   involved   in   the   fact   that   the  con- 
clusions of  imperfect  induction  are  extended  to  unex- 
amined  instances  of  the  phenomenon  in  question? 

6.  What  is  Mill's  position  on  the  validity  of  imperfect  in- 
duction? 

7.  What  influence  does  the  fact  that  a  large  number  of  in- 
stances of  a  phenomenon  have  been  examined  have  on 
the  validity  of  an  inductive  inference? 

8.  What  value  may  we  give  to  number  of  instances  in  an 
inductive  process? 

9.  What  fact  with  respect  to  the  nature  of  induction  is  in- 
volved in  the  hypothetical  character  of  scientific  state- 
ments? 

10.  What  particular  interest  determines  the  use  of  statis- 
tical methods? 

11.  State  and  illustrate  some  of  the  questions  that  statis- 
tical methods  enable  us  to  answer? 

12.  What  purpose  does  the  application  of  statistical  methods 
to  individuals  commonly  serve? 

13.  In  what  respects  do  statistical  conclusions  differ  from 
empirical  generalisations? 

14.  Describe  the  particular  method  of  observation  employed 
by  field  botany,  natural  history  and  descriptive  geology. 

15.  What  are  the  characteristics  of  perception,  and  in  what 
relation  does  perception  stand  to  intelligence? 


SOME  DESCRIPTIVE   METHODS  OF  INDUCTION   405 

16.  In  the  light  of  your  answer  to  the  previous  question, 
what  view  must  be  taken  of  the  logical  function  of  per- 
ception? 

17.  In  what  respects  does  scientific  observation  differ  from 
ordinary  perception? 

18.  What  do  you  understand  by  experimental  observation? 

19.  What  are  the  limits  of  experimental  observation? 

20.  Explain  the  nature  of  theoretical  observation. 

21.  Illustrate  by  reference  to  the  relation  of  the  scientist  to 
his  apparatus  the  place  of  purpose  in  experimental  ob- 
servation. 

22.  'Experimental   observation   involves   a   purposive   inter- 
ference with  the  production  of  phenomena.'     Explain. 

23.  State  what  a  scientist  may  and  may  not  do  in  inter- 
fering with  the  phenomenon  he  wishes  to  observe. 

EXERCISES 

1.  Give  at  least  six  examples  of  empirical  generalisation. 

2.  Give  six  illustrations  of  imperfect  induction,  and  show 
how  each  may  be  used  as  the  basis  of  an  inference. 

3.  Illustrate  from  each  of  the  sciences  you  have  studied 
the  hypothetical  character  of  inductive  inference. 

4.  Show,  by  a  carefully  worked  out  example,  the  nature 
and  method  of  statistical  observation. 

5.  Give  one  example  of  experimental  observation. 

6.  Illustrate  what  is  meant  by  theoretical  observation. 


CHAPTER  XV 

SOME   EXPLANATORY   METHODS   OF   INDUCTION 

The  Nature  of  Scientific  Explanation.  The  meth- 
ods that  were  examined  in  the  last  chapter  may  be 
classified  roughly  as  methods  of  observation,  and 
those  that  are  to  be  examined  in  the  present  chapter 
may  be  classified  approximately  as  methods  of  ex- 
planation. It  will,  perhaps,  help  us  to  understand 
these  latter  methods  if  in  this  section  we  inquire  into 
the  meaning  of  the  term  explanation.  This  is  the 
more  necessary  because  some  confusion  on  this  sub- 
ject has  been  occasioned  by  the  way  in  which  scien- 
tists have  sometimes  expressed  themselves  with 
respect  to  the  aims  of  science.  For  example,  one 
declares  that  science  consists  of  a  complete  descrip- 
tion of  the  phenomena  that  are  brought  under 
observation,  while  another  declares  as  emphatically 
that  description  is  only  a  preliminary  step  in  the 
work  of  the  scientist,  and  that  the  goal  of  all  science 
is  explanation.  If  we  were  to  take  such  statements 
absolutely,  we  should  be  led  to  suppose  that  there 
is  between  the  scientists  an  irreconcilable  differ- 
ence of  opinion  as  to  the  nature  of  the  work  in 
which  they  are  engaged,  and  we  might  presume 
that,  until  they  arrived  at  a  settlement  of  these 
differences,  it  were  useless  for  us  to  discuss  the 
matter  further.  This,  however,  would  be  a  false 
view  to  take;  for  not  only  must  logic  examine  the 

(406) 


SOME  EXPLANATORY  METHODS  OF  INDUCTION     407 

aims  and  methods  of  the  sciences,  but  the  differ- 
ences already  referred  to  are  verbal  rather  than 
real,  and  are  due  in  a  large  measure  to  the  ways  in 
which  what  is  after  all  a  substantial  agreement  has 
happened  to  get  itself  expressed. 

Let  us  first  get  before  ourselves  what  is  meant 
ordinarily  by  a  scientific  explanation,  and  then,  in 
the  light  of  this  information,  we  may  consider  the 
distinction  between  it  and  scientific  observation. 
All  scientific  explanation  conforms  to  a  very  simple 
type;  it  consists  in  stating  what  other  things  occur 
when  the  particular  thing  we  are  observing  occurs. 
If,  for  example,  I  hold  a  book  in  my  hand  and,  re- 
leasing my  grasp  upon  it,  it  falls  to  the  ground,  we 
should  ordinarily  explain  the  falling  of  the  book  to 
the  ground  by  saying  that  I  had  released  my  hold 
upon  it.  The  book  fell  because  I  released  my  hold. 
If,  now,  experimenting  with  other  objects  than 
books,  I  find  that  pencils,  stones,  silverware,  china- 
ware,  etc.,  fall  to  the  ground  when  the  hand  that 
held  them  releases  its  grasp,  I  may  put  the  results 
of  these  observations  into  the  statement  that  'all 
objects  fall  to  the  ground  when  their  support  is  re- 
moved/ If,  further,  the  fall  not  only  of  the  book 
but  of  all  objects  whatsoever  is  connected  with  the 
force  of  gravity,  the  process  of  explanation  has  been 
carried  a  step  farther.  But  however  far  such  a 
process  is  carried,  it  consists  essentially  in  describ- 
ing events  that  occur  along  with  the  event  which,  at 
the  beginning,  was  the  object  of  our  observation. 
This  occurs  when  that  occurs'  is  the  universal  for- 


408  A  TEXT-BOOK   OF  LOGIC 

mula  which  reveals  the  nature  of  scientific  explan- 
ation. 

The  same  view  is  sometimes  expressed  more  pre- 
cisely in  the  statement  that  scientific  explanation 
is  concerned  with  the  discovery  of  the  conditions  of 
the  occurrence  of  any  object  of  observation.  Let 
P  be  the  phenomenon  or  object  observed,  then  the 
question  of  explanation  relates  to  the  conditions,  C, 
under  which  it  occurs.  When  these  conditions  have 
been  discovered  and  recorded,  we  are  said  to  have 
explained  the  phenomenon.  Out  of  the  innumerable 
circumstances  that  accompany  an  event,  the  prob- 
lem of  scientific  explanation  is  to  select  those  which 
must  be  present  whenever  the  event  is  present,  and 
which  when  they  are  absent  the  event  itself  does  not 
occur.  The  factors  of  explanation  are  always 
found  among  the  concomitant  circumstances  of  the 
phenomenon  which  comes  before  us  for  explanation. 
An  examination  and  description  of  these  is  what  is 
meant  by  a  scientific  explanation. 

With  these  statements  in  mind,  we  may  now 
make  clearer  the  distinction  between  scientific  ob- 
servation and  explanation.  It  is  obvious,  in  the 
first  place,  that  the  phenomena  which  we  include 
under  each  of  these  terms  are  continuous  with  each 
other.  For  instance,  the  falling  of  an  object  is  con- 
tinuous with  the  release  of  the  hand's  grasp  upon  it. 
Stated  generally,  a  phenomenon  and  its  conditions 
form  an  inter-connected  series  of  events,  no  one  of 
which  is  unnecessary  to  the  series,  and  each  of  which 
is  important  if  the  series  is  to  maintain  its  essential 


SOME  EXPLANATORY  METHODS  OF  INDUCTION    409 

character.  From  this  point  of  view,  the  distinction 
between  a  phenomenon  and  its  conditions  is  more 
or  less  accidental  and  artificial ;  and  if  we  take  such 
series  as  scientific  units,  regarding  the  objects 
which  are  the  starting  points  of  our  observations 
as  fragments  which  through  scientific  methods  we 
are  to  supplement  by  their  necessary  concomitants, 
we  shall  see  that  the  whole  aim  of  science  has  been 
fulfilled  when  such  a  series  has  received  a  full  and 
complete  description.  If,  in  the  second  place,  we 
do  not  regard  the  object  which  provides  us  with 
the  starting  point  of  our  observation  as  a  fragment, 
but  as  a  phenomenon  which  has  a  quasi-independent 
existence,  we  shall  be  inclined  to  consider  the  search 
for  conditions  as  a  distinct  step  in  scientific  investi- 
gation, and,  laying  emphasis  upon  this,  the  problem 
of  explanation  will  assume  larger  proportions  than 
it  did  in  the  other  view.  But  whichever  of  these 
two  ways  of  looking  at  the  scientific  problem  we 
may  take,  the  factors  of  each  are  the  same,  and  be- 
tween these  views  there  is  only  a  verbal  difference. 
On  either  view,  we  have  to  supplement  what  is 
given  —  the  phenomenon,  with  what  is  not  given  — 
the  conditions;  and  to  determine  the  conditions  of 
a  phenomenon  is  what  we  understand  as  the  prob- 
lem of  scientific  explanation. 

The  Meaning  of  Analogy.  The  word  analogy  is 
used  in  different  senses,  and  these  we  shall  proceed 
to  distinguish.  It  is  used,  in  the  first  place,  to  indi- 
cate an  identity  of  relation.  This  is  the  meaning 
that  it  had  for  Aristotle  with  whom  it  corresponded 


410  A  TEXT-BOOK   OF  LOGIC 

to  mathematical  proportion.  In  this  sense,  it  as- 
sumes the  form  of  2 :  4 : :  3 :  6,  where  the  relation 
between  2 :  4  is  identical  with  the  relation  between 
3 :  6,  and  the  factors  between  which  the  relation 
obtains  are  homogenous.  We  may  state  the  charac- 
teristics of  this  first  meaning  of  analogy  generally 
by  saying  that  whenever  a  is  related  to  b  in  the  same 
way  that  c  is  related  to  d,  then  whatever  follows 
from  a  :  b  follows  also  from  c  :  d,  if  the  inference 
is  based  upon  nothing  but  the  identity  of  the  rela- 
tion between  the  two  pairs  of  factors  or  terms. 

The  word  analogy  is  used,  in  the  second  place, 
to  indicate  a  similarity  of  relation.  The  difference 
between  this  and  the  preceding  use  of  the  term  is 
not  due  to  the  absence  of  proportion,  but  to  the  dif- 
ference in  the  character  of  the  terms  between  which 
the  proportion  obtains.  Although  the  relation  be- 
tween two  pairs  of  terms  is  similar,  the  terms  be- 
tween which  the  relation  holds  may  be  heterogene- 
ous. For  example,  the  number  of  vibrations  per  sec- 
ond of  the  sound  which  is  recognised  by  our  musical 
sense  as  middle  C  (c')  is  261,  that  of  its  octave  (c") 
is  522  (2x261).  The  similarity  of  relations  in- 
volved in  these  facts  is  expressed  in  the  proportion 
261 :  522 : :  c' :  c".  But  since  the  octave  of  any 
musical  note  always  has  twice  as  many  vibrations 
as  the  note  itself,  we  may  express  the  law  of  octaves 
in  the  proportion :  x  vibrations  of  air :  2  x  vibra- 
tions of  air  : :  a  note :  its  octave.  The  analogy  may 
be  interpreted  to  mean  that  the  relation  between 
the  series  of  physical  stimuli  is  connected  in  our 


SOME  EXPLANATORY  METHODS  OF  INDUCTION    411 

knowledge  with  their  corresponding  impressions 
in  such  a  way  that  given  the  former  we  can  infer 
the  latter. 

The  word  analogy  is  used,  in  the  third  place,  to 
indicate  any  resemblance  between  things.  Here  the 
idea  of  proportion  which  was  present  in  the  preced- 
ing uses  has  dropped  out,  and  resemblance  of  any 
kind  between  objects  is  made  the  basis  of  analogical 
inference.  For  example,  certain  resemblances  were 
early  known  to  exist  between  sound  light :  that  both 
were  capable  of  being  reflected,  that  the  direction 
of  reflection  of  each  obeyed  the  same  law,  that  the 
angle  of  reflection  is  equal,  in  each  case,  to  the  angle 
of  incidence.  It  was  further  known  that  sound 
travelled  in  waves.  From  these  data  it  was  inferred 
analogically  that  light  also  travelled  in  waves.  If 
it  had  been  known  that  the  equality  of  the  angles 
of  reflection  and  incidence  in  the  case  of  sound  were 
due  to  its  traveling  in  waves,  the  inference  to  a  like 
mode  of  propagation  in  the  case  of  light  would  have 
been  more  certain.  The  more  important  the  re- 
semblances, that  is  to  say,  the  more  certain  the  in- 
ference. From  the  example  just  used,  the  analogy 
between  things  may  be  expressed  generally  in  the 
following  manner:  If  a  resembles  b  in  certain  re- 
spects, x,  and  a  exhibits  the  character  y,  it  is  in- 
ferred that  b  will  resemble  a  in  possessing  the  char- 
acter y  also. 

The  Logical  Character  of  Analogy.  We  have 
shown  that  analogy  is  a  method  of  inferring  cer- 
tain possible  events  on  the  ground  of  a  resemblance 


412  A  TEXT-BOOK  OF  LOGIC 

between  certain  ascertained  events.  "In  the  syllo- 
gism of  Analogy,"  says  Hegel,  "we  conclude  from 
the  fact  that  some  things  of  a  certain  kind  possess 
a  certain  quality,  that  the  same  quality  is  possessed 
by  other  things  of  the  same  kind."  In  every  argu- 
ment from  analogy  an  identity  of  some  sort  is  as- 
sumed, and  it  is  upon  the  character  of  the  assumed 
identity  that  the  validity  of  the  inference  is  in  every 
case  said  to  depend.  Let  us  look  at  the  soundness 
of  such  arguments  in  the  light  of  this  statement. 

In  the  first  place,  it  is  obvious  that  not  any  kind 
or  degree  of  resemblance  is  a  safe  principle  of  in- 
ference. In  common  life,  we  meet  with  analogical 
arguments  that  are  very  superficial.  For  instance, 
the  loyalty  of  college  students  to  the  university  from 
which  they  were  graduated  may  often  lead  to  a 
mistaken  estimate  of  a  man  who  is  a  graduate  of 
the  same  university.  "It  would  be  a  very  bad  anal- 
ogy," as  Hegel  remarks,  "to  argue  that  since  the 
man  Caius  is  a  scholar,  and  Titus  also  is  a  man, 
Titus  will  probably  be  a  scholar  too;  and  it  would 
be  bad  because  a  man's  learning  is  not  an  uncondi- 
tional consequence  of  his  manhood."  In  public  ad- 
dresses on  political  and  social  questions  we  may 
often  detect  arguments  of  this  sort.  In  the  period 
of  the  Commonwealth  in  England,  the  demand  for 
annual  Parliaments  is  said  to  have  been  urged  on 
the  ground  that  the  serpent  —  which  is  the  wisest 
of  beasts — sheds  his  skin  every  year.  We  also  find 
analogical  reasoning  in  the  works  of  men  of  science, 
and  sometimes  the  conclusion  which  these  argu- 


SOME  EXPLANATORY  METHODS  OF  INDUCTION     413 

ments  are  intended  to  support  rest  upon  a  very 
weak  and  even  false  resemblance.  Take,  for  in- 
stance, the  conception  of  the  human  body  as  a 
machine.  "When  we  desire  to  set  machinery  in 
operation,"  as  Chittenden,  commenting  on  this  view, 
says,  "we  must  get  up  steam,  and  so  a  fire  is  started 
under  the  boiler  and  steam  is  generated  in  propor- 
tion as  fuel  is  burned.  The  source  of  the  energy 
made  use  of  in  moving  the  machinery  is  the  extra- 
neous combustible  material  introduced  into  the  fire- 
box, but  the  energy  of  muscular  contraction,  for 
example,  comes  not  from  the  oxidizable  food  mate- 
rial in  the  stomach,  but  from  the  material  of  the 
muscle  itself.  In  other  words,  in  the  animal  body  it 
is  part  of  the  tissue  framework,  or  material  that  is 
closely  incorporated  with  the  framework,  that  is 
burned  up,  and  the  ability  to  endure  continued  mus- 
cular strain  depends  upon  the  nutritive  condition  of 
the  muscles  involved,  and  not  upon  the  amount  of 
food  contained  in,  or  introduced  into,  the  stomach." 
In  the  second  place,  the  resemblances  upon  which 
analogical  arguments  are  made  to  rest  must  be  im- 
portant resemblances.  Accidental  resemblances  and 
superficial  likenesses  are  at  the  basis  of  all  falla- 
cious reasoning  by  analogy.  With  this  class  of  anal- 
ogies in  mind  Heine  was  led  to  exclaim,  "Heaven 
defend  us  from  the  Evil  One  and  from  metaphors." 
But  if  the  resemblance  is  essential  and  important, 
there  is  no  need  to  avoid  the  use  of  this  method  of 
reasoning.  Now  when  we  speak  of  a  resemblance 
being  essential,  we  mean  that  the  characteristics 


414  A   TEXT-BOOK   OF   LOGIC 

with  respect  to  which  objects  are  compared  must  be 
essential  either  to  the  existence  of  the  objects  or  to 
the  purpose  which  these  objects  realise.  If,  to  illus- 
trate the  former  case,  we  infer  that  certain  things 
are  true  of  diamonds  because  they  are  true  of 
graphite,  we,  no  doubt,  do  so  with  the  thought  in 
mind  that  these  substances  are  different  forms  of 
carbon.  To  illustrate  the  latter,  we  may  argue  from 
the  similarity  in  shape  of  certain  flints  found  in  the 
ground  and  those  used  by  certain  savage  tribes  of 
the  present  day  that  the  former  were  used  as 
weapons  since  this  is  the  use  that  the  latter  are 
known  to  have. 

In  the  third  place,  analogical  arguments  must 
take  into  account  not  only  the  importance  of  the 
resemblances  but  the  non-importance  of  the  differ- 
ences between  the  objects  compared.  An  interest- 
ing example  is  the  following,  borrowed  from  Gib- 
son. He  says,  "we  might  enumerate  many  points 
of  external  resemblance  between  the  Whale  and  the 
Shark,  and  found  upon  them  an  analogical  argu- 
ment to  the  effect  that  the  respiration-processes  in 
the  two  animals  must  be  similar.  The  whale,  we 
might  say,  resembles  the  shark  not  only  in  all  the 
common  characters  of  Vertebrates,  but  also  in  its 
submarine  habitat  and  in  being  (as  regard  species) 
one  of  the  very  largest  of  marine  animals.  Like  the 
shark,  it  is  fish-like  in  external  form,  its  fusiform 
body  being  well  fitted  for  cleaving  the  water.  An- 
teriorly its  body  passes  into  the  head  without  any 
distinct  neck,  and  posteriorly  it  is  furnished  with  a 


SOME  EXPLANATORY  METHODS  OF  INDUCTION     415 

swimming-tail  into  which  the  body  gradually  tapers. 
It  has  no  hairy  covering.  Like  the  shark,  again, 
it  has  a  wide  mouth,  and  it  is  of  predaceous  habit, 
feeding  only  on  living  animal  nutriment.  There- 
fore we  may  with  great  probability  conclude  that 
its  method  of  respiration  is  like  that  of  the  shark— 
i.  e.,  that  it  breathes  the  oxygen  dissolved  in  the 
water,  and  has  no  need  to  be  supplied  with  atmos- 
pheric air. 

"But  this  argument  would  be  unsound.  The  points 
that  we  ought  to  have  observed  are  the  characters 
connected  with  the  function  of  respiration.  The 
presence  of  gill-slits  in  the  shark  and  their  absence 
in  the  whale  is  a  difference  so  essential  to  the  in- 
quiry that  its  observation  would  at  once  have  been 
sufficient  to  make  our  analogy  fall  to  the  ground. 
And  among  the  still  more  obvious  external  differ- 
ences there  is  a  single  character  which  also  should 
alone  outweigh  all  the  above  mentioned  resem- 
blances. The  extremity  of  the  shark's  tail  is  ex- 
panded vertically ;  in  the  whale  the  flukes  of  the  tail 
are  placed  horizontally.  From  many  points  of  view 
this  difference  might  be  regarded  as  unimportant; 
but  from  the  point  of  view  of  our  analogical  argu- 
ment it  is  very  important  indeed,  for  it  is  intimately 
connected  with  the  problematic  point  of  resemblance 
that  we  are  endeavouring  to  establish.  For  sea- 
creatures  which,  like  the  whale  and  the  shark,  spend 
their  life  in  swimming  freely  through  the  water, 
the  direction  of  movement  is  chiefly  determined  by 
the  presence  or  absence  of  the  air-breathing  habit. 


416  A  TEXT-BOOK   OF  LOGIC 

Those  creatures  that  have  no  need  of  atmospheric 
air  move  usually  in  straight-forward  and  lateral 
directions,  and  for  effecting  such  movements  a  ver- 
tically expanded  caudal  fin  is  admirably  fitted.  But 
creatures  that  need  to  rise  frequently  to  the  surface 
of  the  water  for  the  purpose  of  respiration  are  con- 
stantly moving  upward  and  downward.  To  move- 
ments of  this  kind  a  tail  with  horizontally  expanded 
fluxes  is  precisely  adapted.  Thus  the  whale's  hori- 
zontally expanded  tail  affords  a  strong  presumption 
in  favour  of  the  presence  of  the  air-breathing  habit ; 
and  this  apparently  trifling  difference  between  the 
two  creatures  must  be  regarded  as  fatal  to  the 
cogency  of  the  analogical  argument." 

The  Function  of  Analogy  in  Induction.  We  have 
been  considering  analogy  as  a  special  kind  of  argu- 
ment, the  way  in  which  Aristotle  understood  it.  We 
proceed  now  to  discuss  the  value  that  analogies  have 
for  advancing  our  knowledge  of  the  world  about  us, 
the  assistance  they  may  give  in  the  problem  of  ex- 
planation. Analogy,  as  our  exposition  has  shown, 
is  an  argument  from  similar  instances.  It  is,  to 
quote  Mellone,  "any  resemblance  between  things 
which  enables  us  to  believe  of  one  what  we  know 
of  the  other."  We  advance  from  one  instance  to 
another  on  the  basis  of  a  perceived  or  imagined  sim- 
ilarity between  the  instances.  The  necessity  of  ad- 
vancing in  an  analogical  argument  from  particular 
to  particular,  has  led  to  the  saying  that  analogy 
"sticks  in  the  particular  instances."  Although  this 
is  true,  it  is  not  on  that  account  worthless  as  an  in- 


SOME  EXPLANATORY  METHODS  OF  INDUCTION    417 

strument  or  means  of  arriving  at  the  law  of  the 
connection  between  resembling  instances.  For  if 
there  is  a  resemblance,  or  a  group  of  resemblances, 
between  P  and  P',  such  that  we  feel  warranted  in 
affirming  of  P'  what  we  know  positively  only  of  P, 
we  may  look  upon  the  similarity,  not  merely  as  a 
bridge  from  the  one  instance  (P)  to  the  other  (P')> 
but  as  a  suggestion  of  a  specific  connection  between 
the  two  instances  which  is  not  brought  out  ex- 
plicitly by  the  analogy.  It  is  this  characteristic  of 
suggesting  more  than  it  can  possibly  make  clear, 
that  renders  analogy  of  service  in  an  inductive  proc- 
ess. The  following  remarks  are  intended  to  make 
this  point  clear. 

Two  things  are  characteristic  of  analogy.  In  the 
first  place,  the  comparison  of  instances,  as  we  have 
seen,  rests  upon  what  are  called  their  essential 
attributes,  but,  in  the  second,  the  degree  of  the 
resemblance  always  remains  more  or  less  undeter- 
mined. When  we  have  assured  ourselves  that  the 
resemblance  depends  upon  essential  features  of  the 
compared  phenomena,  we  are,  however,  still  in 
doubt  about  the  precise  factor  or  factors  in  the  re- 
semblance upon  which  the  inferred  characteristic 
really  depends.  Thus  any  two  phenomena,  P  and 
P',  may  resemble  each  other  in  possessing  the 
attribute  x,  a  resemblance  which  seems  to  warrant 
us  in  expecting  that  if  P  also  shows  the  character- 
istic y,  P'  will  likewise  show  the  same  characteristic. 
To  take  a  concrete  example.  The  chemist  classifies 

27 


418  A  TEXT-BOOK  OF  LOGIC 

a  number  of  elements  together  under  the  head  of 
alkaline  metals  because  all  these  elements  —  potas- 
sium, sodium,  caesium,  rubidium,  and  lithium,  - 
possess  certain  characteristics  in  common;  for  in- 
stance, their  active  combination  with  oxygen  to  de- 
compose water  at  all  temperatures;  their  forming 
strongly  basic  oxides,  highly  soluble  in  water,  yield- 
ing powerful  caustic  and  alkaline  hydrates  from 
which  water  can  not  be  expelled  by  heat;  the  solu- 
bility of  their  carbonates  in  water;  and  the  forma- 
tion by  each  metal  of  only  one  chloride.  Now,  if  in 
the  progress  of  the  chemistry  of  any  one  of  these 
metals  a  new  property  is  discovered,  it  is  natural 
to  infer  by  analogy  that  the  other  members  of  the 
group  will  display  under  appropriate  conditions  the 
same  property.  But  beyond  the  suggestion  of  a 
connection  of  the  new  property  with  the  character- 
istics of  the  alkaline  group  analogy  cannot  go;  it 
cannot  point  out  on  which  attribute,  or  combination 
of  essential  attributes,  the  new  property  really  de- 
pends. Thus  an  argument  by  analogy  presumes  a 
connection  between  x  and  y,  but  it  cannot  show  that 
y  depends  on  x  rather  than  on  some  other  property 
in  P  which  may  not  belong  to  what  we  have  called 
its  essential  attributes.  However  strong  the  pre- 
sumption may  be  that  x  and  y  are  causally  related, 
there  always  remains  the  possibility  that  y  is  condi- 
tioned in  some  other  way.  Analogical  arguments 
for  this  reason  are  never  conclusive,  and  in  an  in- 
ductive process  they  are  valuable  only  because  they 
suggest  lines  of  further  observation  which  may 


SOME  EXPLANATORY  METHODS  OF  INDUCTION    419 

either  verify  or  discredit  the  analogical  inference. 
Mill,  therefore,  is  right  when  he  regards  an  analogy 
as  "a  mere  guide  post,  pointing  out  the  direction 
in  which  more  vigorous  investigations  should  be 
prosecuted.  It  is  in  this  last  respect,"  says  Mill, 
"that  considerations  of  analogy  have  the  highest 
scientific  value.  The  cases  in  which  analogical  evi- 
dence affords  in  itself  any  very  high  degree  of  prob- 
ability are,  as  we  have  observed,  only  those  in 
which  the  resemblance  is  very  close  and  extensive; 
but  there  is  no  analogy,  however  faint,  which  may 
not  be  of  the  utmost  value  in  suggesting  experi- 
ments or  observations  that  may  lead  to  more  posi- 
tive conclusions."  With  this  view,  to  which  Mill 
does  not  consistently  adhere,  Jevons  is  in  agree- 
ment, and  he  has  made  it  the  foundation  of  his  chap- 
ter on  analogy  in  the  Principles  of  Science. 

Nature  of  Hypothesis.  An  hypothesis  is  an  at- 
tempted explanation  of  an  occurrence,  a  supposition 
about  the  connection  of  particular  phenomena.  To 
get  the  meaning  of  this  general  statement  before  us, 
let  us  consider  a  particular  case.  Malaria  is  a  dis- 
ease which  has  a  set  of  characteristic  symptoms, 
the  chief  of  which  are  chills  and  fever  occurring  at 
more  or  less  definite  intervals  of  time.  When  the 
physician  has  become  familiar  with  the  character- 
istic symptom  complex  of  the  disease,  he  is  able  to 
diagnose  the  new  cases  that  come  under  his  obser- 
vation by  means  of  the  similarity  that  they  bear  to 
this  complex ;  all  the  cases  that  show  the  diagnostic 
marks  of  the  disease  he  calls  malaria.  The  logical 


420  A  TEXT-BOOK   OF  LOGIC 

procedure  in  this  instance  is  analogical.  If,  how- 
ever, instead  of  taking  the  physician's  attitude  which 
requires  him  to  diagnose  only  for  the  purpose  of 
selecting  the  proper  remedies,  we  approach  the  dis- 
ease from  the  standpoint  of  the  scientist  who  wants 
to  know  what  malaria  is,  we  shall  have  to  go  beyond 
the  similarities  which  figure  in  the  physician's  diag- 
nosis, and,  by  a  series  of  suppositions  or  hypotheses, 
work  our  way  among  the  antecedents  and  concomi- 
tants of  the  cases  of  the  disease  for  some  clue  to  the 
agent  which  is  responsible  for  the  production  of  the 
disease.  It  is  not  enough  to  say  that  similar  symp- 
toms mean  the  same  disease,  the  question  we  are  now 
asking  is  what  produces  the  similar  symptoms  in  all 
the  cases  that  occur.  We  are  looking  for  something 
more  than  similarity,  we  are  searching  for  an  iden- 
tity among  the  conditions  under  which  the  disease 
is  contracted.  Thus,  for  example,  night  air,  damp 
places,  exhalations  from  marshy  ground  have  been 
proposed  as  the  antecedent  condition  which  is 
capable  of  producing  malarial  fever.  It  is  only 
within  comparatively  recent  times  that,  for  these 
hypotheses,  another  has  been  substituted  which  con- 
nects the  disease  with  the  bite  of  the  Anopheles 
mosquito,  and  this  is  the  view  that  is  held  at  the 
present  day.  The  bite  of  the  Anopheles  mosquito* 
is  our  hypothesis  for  the  occurrence  of  malaria. 

In  the  light  of  this  illustration,  we  may  observe 
that  not  any  supposition  about  phenomena  is  an 
hypothesis.  It  is  only  when  the  supposition  points 
us  to  phenomena  of  the  same  order  as  the  event 


SOME  EXPLANATORY  METHODS  OF  INDUCTION     421 

that  we  are  trying  to  explain  that  it  satisfies  the 
conditions  of  a  tenable  hypothesis.  In  medicine, 
for  example,  we  no  longer  entertain  theological  ex- 
planations of  disease,  and  for  devils  we  are  substi- 
tuting bacteria  and  their  toxins,  and  in  those  dis- 
eases which  cannot  be  shown  to  be  of  bacterial 
origin,  as  for  example  many  of  the  occupational 
diseases,  we  assign  either  a  chemical  cause,  as  in 
lead  poisoning,  or  a  mechanical  one,  as  in  the  dis- 
ease characteristic  of  the  Sheffield  steel  grinders. 
When  made  with  regard  to  the  requirement  we  are 
now  considering,  namely,  that  the  supposition 
should  be  stated  in  terms  of  the  same  order  as  the 
phenomenon  to  be  explained,  hypotheses  differ  from 
one  another  only  in  the  degree  of  their  probability; 
and  it  seems  to  us  to  be  quite  misleading  to  speak  of 
them  as  guesses,  as  is  done  by  some  logicians,  as  if 
they  were  altogether  uncontrolled  by  the  nature  of 
the  phenomena  for  which  an  explanation  is  being 
sought.  The  truth  of  this  statement  is  apparent 
when  we  recognise  that  the  demand  for  an  hypoth- 
esis is  only  a  particular  form  of  the  demand  for  a 
careful  analysis  of  the  phenomena  under  observa- 
tion. Our  acquaintance  with  objects  becomes  more 
minute  as  well  as  more  accurate  under  the  stimulus 
that  comes  from  the  call  for  explanation ;  and  if  one 
step  in  the  process  of  explanation  is  hypothetical, 
that  step  must  still  be  controlled  by  the  nature  of 
the  observed  material  if  we  are  to  safeguard  the  in- 
ductive process  against  useless  and  irresponsible 
guesses.  The  satisfaction  of  this  requirement  by 


422  A  TEXT-BOOK  OF  LOGIC 

science  may  be  briefly  illustrated.  To  account  for 
the  phenomena  of  sound,  the  physicist,  starting  with 
the  sound  experience,  connects  this  with  the  undu- 
lations of  the  air  which  occasion  it,  and  these  undu- 
lations, again,  he  connects  with  a  vibrating  body,  — 
a  stretched  string,  the  vocal  cords,  an  organ  pipe. 
When  the  scientist  asks  what  is  the  source  of  the 
phenomena  of  light  which  occasion  the  sensation  of 
vision,  although  he  cannot  point  definitely  to  the 
material  bodies  which  produce  the  undulations  in 
the  ether,  he  forms  his  hypothesis  in  terms  of  the 
same  order  as  the  phenomena  that  he  has  under  in- 
vestigation; and  he  does  so  because  the  "scientific 
imagination,"  to  quote  Tyndall,  "demands,  as  the 
origin  and  cause  of  a  series  of  ether-waves,  a  par- 
ticular vibrating  matter  quite  as  definite,  though  it 
may  be  excessively  minute,  as  that  which  gives 
origin  to  a  musical  sound.  Such  a  particle  we  name 
an  atom  or  a  molecule.  I  think  the  intellect,  when 
focussed  so  as  to  give  definition  without  penumbral 
haze,  is  sure  to  realize  this  image  at  last." 

Objections  to  the  Use  of  Hypothesis.  Although 
the  history  of  modern  science  furnishes  so  many 
illustrations  of  the  value  of  hypotheses,  and  al- 
though the  methods  in  use  at  the  present  day  for 
the  advancement  of  scientific  knowledge  depend 
also  upon  their  employment,  there  is,  nevertheless, 
among  scientific  men  either  only  a  half-hearted 
recognition  of  their  services,  or  a  misleading  rejec- 
tion of  their  claims  to  a  place  in  scientific  procedure. 
This  interesting  fact  is  not  difficult  to  understand, 


SOME  EXPLANATORY  METHODS  OF  INDUCTION     423 

and  we  refer  to  it  here  because  it  enables  us  to 
explain  some  aspects  of  the  formation  of  hypoth- 
eses which  as  yet  have  not  been  mentioned.  The 
hesitancy  of  men  of  science  to  recognise  that  the 
advancement  of  scientific  knowledge  is,  in  any  re- 
spect, dependent  upon  hypotheses,  may  be  attrib- 
uted to  their  effort  to  exclude  from  all  parts  of  their 
work  influences  and  additions  that  are  derived  from 
the  nature  of  the  mental  processes  through  which 
that  work  is  carried  on.  The  aim  of  science  is 
throughout  objective  in  the  sense  that  its  task  is  to 
describe  and  explain  the  facts  of  observation,  to 
arrive  at  judgments  about  these  facts  that  are  inde- 
pendent of  the  idiosyncrasies  of  the  individual  mind. 
"The  scientific  man,"  as  Karl  Pearson  says,  "has 
above  all  things  to  strive  at  self-elimination  in  his 
judgments,  to  provide  an  argument  which  is  as  true 
for  each  individual  mind  as  for  his  own."  The 
life  of  science  depends  upon  loyalty  to  this  aim. 
The  intellectual  integrity  of  every  scientific  man  is 
involved  in  his  efforts  to  maintain  this  aim.  All 
this  may  be  granted;  it  may  even  be  admired  and 
praised.  And  yet  we  cannot  avoid  the  impression 
that  if  the  spirit  of  loyalty  to  professional  ideals 
which  is  displayed  by  workers  in  the  fields  of  the 
particular  sciences  were  supplemented  by  an  ac- 
quaintance with  the  history  of  scientific  achieve- 
ments, the  objections  to  hypothesis  would  be  miti- 
gated, and  in  time  might  entirely  disappear.  For 
the  admission  of  hypothesis  in  no  way  interferes 
with  keeping  the  work  of  science  objective,  and 


424  A  TEXT-BOOK  OF  LOGIC 

their  practical  rejection  may  often  render  impos- 
sible of  realisation  the  aims  which  stimulate  scien- 
tific effort. 

The  situation  that  has  just  been  described  may 
be  made  more  explicit  by  saying  that  without  an 
active  and  fertile  imagination,  it  is  impossible  to 
formulate  a  satisfactory  hypothesis.  It  is,  in  part, 
because  the  scientist  does  not  take  the  pains  to 
ascertain  what  are  the  nature,  conditions,  and  limits 
of  the  imagination  that  he  looks  askance  upon  the 
formation  of  hypotheses.  This  is  not  the  place  to 
state  and  develop  a  doctrine  of  the  imagination;  it 
is  enough  for  our  purpose  to  call  attention  to  the 
fact  that  many  of  the  leading  men  of  science  have 
borne  eloquent  testimony  to  the  value  of  the  imagi- 
nation in  advancing  the  interests  of  scientific  truth. 
In  his  address  on  'Scientific  Use  of  the  Imagination/ 
Tyndall  writes:  "Bounded  and  conditioned  by  co- 
operant  reason,  imagination  becomes  the  mightiest 
instrument  of  the  physical  discoverer.  Newton's 
passage  from  a  falling  apple  to  a  falling  moon  was, 
at  the  outset,  a  leap  of  the  imagination."  Tyndall 
prefixed  to  his  essay  the  following  passage  from  an 
address  to  the  Royal  Society  by  Sir  Benjamin  Brodie. 
"Lastly,  physical  investigation,  more  than  anything 
besides,  helps  to  teach  us  the  actual  value  and  right 
use  of  the  Imagination  —  of  that  wonderful  faculty 
which,  left  to  ramble  uncontrolled  leads  us  astray 
into  a  wilderness  of  perplexities  and  errors,  a  land  of 
mists  and  shadows;  but  which,  properly  controlled 


SOME  EXPLANATORY  METHODS  OF  INDUCTION     425 

by  experience  and  reflection,  becomes  the  noblest 
attribute  of  man;  the  source  of  poetic  genius,  the 
instrument  of  discovery  in  Science,  without  the  aid 
of  which  Newton  would  never  have  invented  flux- 
ions, nor  Davy  have  decomposed  the  earths  and 
alkalies,  nor  would  Columbus  have  found  another 
continent."  In  his  Methods  and  Results,  Huxley 
writes :  "It  is  a  favourite  popular  delusion  that  the 
scientific  inquirer  is  under  a  sort  of  moral  obliga- 
tion to  abstain  from  going  beyond  that  generalisa- 
tion of  observed  facts  which  is  absurdly  called 
'Baconian'  induction.  But  any  one  who  is  practically 
acquainted  with  scientific  work  is  aware  that  those 
who  refuse  to  go  beyond  fact  rarely  gets  as  far  as 
fact;  and  any  one  who  has  studied  the  history  of 
science  knows  that  almost  every  great  step  therein 
has  been  made  by  'anticipation  of  nature/  that  is, 
by  the  invention  of  hypotheses  which,  though  veri- 
fiable, often  had  little  foundation  to  start  with,  and 
not  infrequently,  in  spite  of  a  long  career  of  useful- 
ness, turned  out  to  be  wholly  erroneous  in  the  long 
run." 

These  quotations  are  sufficient  to  illustrate  the 
importance  of  the  imagination  in  the  construction 
of  scientific  hypotheses,  and  to  indicate  the  reason 
why  many  men  of  science  look  with  suspicion  upon 
the  use  of  hypotheses.  "Scientific  men  fight  shy  of 
the  word  (imagination)  because  of  its  ultra-scien- 
tific connotations,"  because  its  use  is  often  uncon- 
trolled, and  because  under  the  best  conditions  it 
sometimes  leads  us  astray.  But  to  reject  an  instru- 


426  A  TEXT-BOOK  OF  LOGIC 

ment  of  research  because  of  its  limitations  is  no 
more  reasonable  than  would  be  a  physician's  refusal 
to  employ  strychnine  in  the  cure  of  a  patient,  be- 
cause that  drug  is  on  the  commercial  market  in  the 
form  of  'Rough  on  Rats.'  We  are  not  advocating  an 
indiscriminate  exercise  of  the  imagination,  nor  the 
substitution  of  it  for  the  careful  and  painstaking 
observation  of  phenomena.  What  we  are  pointing 
out  is  that  there  are  conditions  of  physical  investi- 
gation which  render  all  known  instruments  of  pre- 
cision inadequate  and  clumsy  tools,  and  that  if 
observation  is  not  to  be  hindered  its  range  must  be 
extended  as  far  beyond  that  of  our  instrumental 
world  as  this  is  beyond  the  world  made  known  by 
our  natural  organs  of  perception.  We  cannot,  for 
example,  bring  under  observation  by  the  most 
powerful  microscope  the  particles  of  matter  which 
are  the  media  in  our  atmosphere  of  reflected  light. 
By  what  means  has  the  existence  of  such  particles 
scattered  throughout  our  space  come  to  be  believed 
in?  Tyndall  cites  this  example  as  an  illustration 
of  the  use  that  science  may  make  of  the  imagina- 
tion, as  he  does  also  Darwin's  hypothesis  of  a  pri- 
mordial germ  as  the  source  of  all  the  variety  of 
organisms  now  upon  the  earth's  surface.  These  in- 
stances, and  many  others  that  are  among  the  most 
brilliant  achievements  of  science,  lead  us  to  look 
upon  the  imagination  as  itself  an  instrument  of 
observation,  and  in  the  form  of  carefully  stated 
hypothesis,  it  leads  to  an  explanation  of  many  ob- 


SOME  EXPLANATORY  METHODS  OF  INDUCTION     427 

served  facts  which  without  its  aid  would  postpone 
indefinitely  important  lines  of  research. 

Verification  of  Hypotheses.  If  we  are  to  carry 
our  explanations  of  events  to  a  successful  termina- 
tion, the  hypotheses  by  means  of  which  the  rela- 
tions of  particular  phenomena  are  brought  under  an 
intelligible  view  need  to  be  tested  and  not  merely 
stated,  to  be  verified,  not  merely  formulated.  There 
are  two  steps  in  the  process  of  verification  to  which 
we  may  give  attention.  "To  prove  or  disprove  (an) 
induction  we  must  have  resort,"  says  Tyndall,  "to 
deduction  and  experiment."  Mill's  definition  of  an 
hypothesis,  that  it  is  "any  supposition  which  we 
make  (either  without  actual  evidence,  or  on  evidence 
avowedly  insufficient)  in  order  to  endeavour  to 
deduce  from  it  conclusions  in  accordance  with  facts 
known  to  be  real,"  points  to  the  same  two  require- 
ments. An  hypothesis  which  is  not  capable  of  be- 
ing verified  would  serve  no  immediate  purpose,  and 
whether  it  serves  any  purpose  at  all  need  not  con- 
cern us.  We  are  now  studying  living  hypotheses, 
those  which  answer  questions,  and  render  intelli- 
gible the  particular  facts  of  observation.  And  it  is 
about  these  that  we  are  warned  that  it  is  not  their 
intelligibility  merely,  and  not  the  fact  that  they 
answer  questions,  which  recommends  them  finally  to 
our  acceptance.  It  is  only  if  our  hypotheses  are 
true,  if  they  make  us  acquainted  with  the  actual 
relations  which  objects  sustain  to  one  another,  that 
they  are  received  as  part  of  our  scientific  knowledge. 
The  formation  of  hypotheses  takes  us  beyond  what 


428  A  TEXT-BOOK  OF  LOGIC 

is  actually  known  and  observed,  and  for  this  reason 
there  is  in  every  hypothesis  an  element  of  risk ;  but 
they  must  at  the  same  time  make  it  possible  for  us 
to  return  to  fact  and  the  observation  of  fact,  and  it 
is  this  that  renders  them  useful  in  the  advancement 
of  human  knowledge.  The  return  to  fact  is  made 
in  the  two  steps  of  deduction  and  experiment. 

Let  us  take  as  an  illustration  of  these  two  stages 
in  the  process  of  verification  the  well-known  fact 
that  water  rises  to  a  certain  height  in  a  pump,  and 
the  explanation  of  this  fact  on  the  ground  that 
"Nature  abhors  a  vacuum."  The  story  goes  that  in 
trying  to  raise  water  to  a  great  elevation,  some 
Florentine  gardeners  found  that  the  column  of 
water  ceased  at  the  height  of  thirty-two  feet.  The 
matter  was  referred  to  Galileo  who,  embittered  by 
the  reception  that  had  been  accorded  to  his  science, 
said  that  he  supposed  that  Nature  abhorred  a 
vacuum  only  at  the  height  of  thirty-two  feet.  It 
was  left  for  Toricelli,  Galileo's  pupil,  to  provide  an 
answer  to  the  inquiry.  He  supposed  that  water 
might  be  forced  into  a  tube  by  pressure  on  the  sur- 
face of  the  liquid  outside.  After  much  thought,  it 
occurred  to  Toricelli  that  the  atmosphere  might 
exert  such  pressure,  and  that  the  column  of  water 
thirty-two  feet  in  height  might  be  the  exact  weight 
necessary  to  equalise  this  atmospheric  pressure. 
This  supposition  was  Toricelli's  hypothesis.  Was  it 
true?  This  was  the  next  question  that  the  physicist 
confronted,  and  it  is  exceedingly  instructive  to  ob- 
serve the  way  he  went  to  work  to  verify  his  hypoth- 


SOME  EXPLANATORY  METHODS  OF  INDUCTION    429 

esis.  He  deduced  certain  consequences  from  the 
hypothesis.  He  argued  that  if  thirty-two  feet  of 
water  will  hold  the  atmospheric  pressure  in  equili- 
brium, a  shorter  column  of  a  heavier  liquid  should  do 
the  same.  According  to  his  calculations,  mercury, 
which  is  thirteen  times  heavier  than  water,  should 
be  able  to  balance  the  pressure  of  the  atmosphere 
at  thirty  inches.  The  next  step  in  the  process  of 
verifying  the  original  hypothesis  was  an  experi- 
ment. Toricelli  filled  a  glass  tube  a  yard  or  so  in 
length,  open  at  one  end  and  closed  at  the  other, 
with  mercury.  Placing  his  thumb  over  the  open 
end,  he  inverted  it  in  a  bath  filled  with  the  same 
metal.  When  he  removed  his  thumb,  the  mercury 
began  to  sink,  and  continued  to  sink  until  the  height 
of  thirty  inches  had  been  reached.  The  proof  of  the 
hypothesis  was  complete. 

Hypothesis  and  Theory.  The  difference  between 
an  hypothesis  and  a  theory  is  a  relative  one  merely. 
To  bring  out  this  feature  of  the  terms'  meanings, 
we  may  say  that  a  theory  is  a  completely  verified 
hypothesis,  and  that  an  hypothesis  is  an  incom- 
pletely verified  theory.  This  statement  will  have 
served  its  purpose  if  it  remind  us  that  hypothesis  and 
theory  both  spring  out  of  the  demand  for  explana- 
tion, that  they  both  involve  the  use  of  the  creative 
imagination  for  their  formation,  and  call  for  verifi- 
cation in  the  way  that  has  been  described.  It  is  these 
similarities  which  justifies  the  popular  use  of  the 
terms  as  synonymous.  It  will  be  useful  for  us,  how- 
ever, to  look  at  the  matter  a  little  more  closely.  We 


430  A  TEXT-BOOK   OF  LOGIC 

may  observe,  for  instance,  that  we  advance  from 
hypothesis  to  theory,  not  by  leaving  our  hypothesis 
behind,  but  by  developing  it  in  the  light  of  further 
experiences  so  as  to  make  it  accord  with  facts  hith- 
erto not  known  or  not  understood.  In  this  sense,  the 
hypothesis  becomes  a  theory.  To  illustrate,  when  ice- 
cold  water  is  poured  into  a  glass  on  a  hot  summer 
day,  little  drops  of  water  collect  and  trickle  down  on 
the  outside  of  the  glass.  How  do  we  account  for  this 
phenomenon  ?  The  sudden  cooling  of  the  glass  takes 
place  by  radiation  of  its  heat,  and  the  water-vapour 
of  the  atmosphere  condenses  on  the  cooled  surface 
of  the  glass.  The  same  hypothesis  may  be  extended 
to  account  for  the  formation  of  dew,  and  a  number 
of  other  phenomena.  An  hypothesis  that  can  be 
used  to  explain  a  variety  of  facts  which  were  not 
thought  of  when  the  hypothesis  was  formulated,  can 
justly  be  regarded  with  greater  confidence  than  one 
which  explains  only  a  single  phenomenon.  Every 
new  fact  which  fits  into  an  hypothesis  strengthens 
it.  At  first,  an  hypothesis  has  an  explanatory  value 
only  for  the  particular  phenomenon  with  respect  to 
which  it  is  framed.  But  if  an  hypothesis  is  ca- 
pable of  growth,  both  in  respect  to  the  number  and 
variety  of  the  facts  which  it  is  capable  of  explain- 
ing, and  in  the  simplicity  of  the  form  which  it  as- 
sumes, the  conditions  are  present  for  the  develop- 
ment of  the  hypothesis  into  what  is  known  as  a 
theory.  We  speak,  for  example,  of  the  Darwinian 
hypothesis,  because  the  supposition  it  states  is  still 
in  a  condition  of  growth,  and  because  the  modifica- 
tions which  are  being  introduced  into  Darwin's 


SOME  EXPLANATORY  METHODS  OF  INDUCTION    431 

statement  are  intended  to  make  his  view  harmonise 
more  fully  with  progressive  experience  and  recent 
discovery.  When,  however,  we  regard  the  idea  of 
growth  throughout  the  known  world  as  a  confirmed 
doctrine  of  science,  we  no  longer  speak  of  the  Dar- 
winian hypothesis,  but  of  the  theory  of  evolution. 
In  the  same  way,  and  for  similar  reasons,  we  speak 
of  the  theory  of  gravitation,  the  Copernican  theory, 
the  theory  of  the  conservation  of  energy.  What 
we  mean  by  such  designations  is  that  the  evidence 
for  the  particular  hypotheses  which  lies  back  of 
them  is  ample  and  varied,  that  the  exceptions  within 
the  fields  of  their  application  are  either  insignficant 
or  are  absent  altogether,  that  newer  experiences 
and  discoveries  tend  to  confirm  these  views.  When 
lines  of  evidence  tend  to  converge  and  to  be  f  ocussed 
on  an  hypothesis,  that  hypothesis  has  no  longer  the 
tentative  position  of  a  supposition,  but  the  firmer 
and  surer  foundation  of  a  confirmed  belief.  The 
formulation  of  such  a  confirmed  belief  is  called  a 
theory. 

REFERENCES 

H.  A.  Aikins,  The  Principles  of  Logic,  Ch.  XXV. 

B.  Bosanquet,  The  Essentials  of  Logic,  Lecture  X.,  Ch.  I., 

e-b,  3. 
J.  E.   Creighton,   An   Introductory  Logic,   3d   Edition,   Chs. 

XIV.,  XV.,  XVIII.,  XIX. 
J.  G.  Hibben,  Logic  Deductive  and  Inductive,  Part  II.,  Chs. 

IIIc,  XL,  XII.,  XIII.,  XIV. 
W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Lessons  XXVI., 

XXVII. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  VIII.,  §§  4-8. 


432  A  TEXT-BOOK  OF  LOGIC 

W.  Minto,  Logic,  Inductive  and  Deductive,  Chs.  IX.,  X. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Chs. 

XV.,  §§  5-7,  XVIIL,  XIX.,  XX. 
W.  J.  Taylor,  Elementary  Logic,  Chs.  XV.,  XVI. 

ADVANCED 

B.  Bosanquet,  Logic,  Vol.  II.,  Book  II.,  Chs.  II.,  III.,  IV.,  V. 
W.  R.  B.  Gibson,  The  Problem  of  Logic,  Chs.  XXXVIII., 

XLII. 
W.  S.  Jevons,  The  Principles,  of  Science,  Chs.  XVIIL,  XIX., 

XXIII.,  XXIV.,  XXVI.,  XXVII.,  XVIIL 
H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Ch.  XXI. 
H.  Lotze,  Logic,  Vol.  II.,  Book  II.,  Chs.  VIII.,  IX. 
J.  S.  Mill,  A  System  of  Logic,  Book  III.,  Chs.  VII.,  XIV., 

XX.,  XXIII. 

F.  C.  S.  Schiller,  Formal  Logic,  Chs.  XIX.,  XXII. 
J.  Venn,  Empirical  Logic,  Chs.  XVI.,  XXI. 
J.  Welton,  A  Manual  of  Logic,  Vol.  II.,  Book  V.,  Chs.  III., 

§§  147,  149,  IV.,  V.,  §§  153,  154,  VII. 

QUESTIONS 

1.  Is   there   necessarily   any   irreconcilable   opposition   be- 
tween the  view  that  the  aim  of  science  is  complete  ob- 
servation, and  that  it  is  explanation?     Explain. 

2.  To  what  simple  type  does  all  scientific  explanation  con- 
form?   Illustrate. 

3.  What  is  meant  by  saying  that  explanation  consists  in 
discovering   the   conditions   of  the   occurrence   of   phe- 
nomena? 

4.  Are  all  the  circumstances  attending  the  occurrence  of 
an  event  conditions  of  its  occurrence? 

5.  What  is  meant  by  saying  that  the  phenomena  of  ob- 
servation and  those  of  explanation  are  continuous  with 
each  other? 

6.  What  bearing,  if  any,  do  the   facts  included   in  your 
answer  to   the   previous   question   have   upon   the   dis- 
tinction between  a  phenomenon  and  its  conditions? 


SOME  EXPLANATORY  METHODS  OF  INDUCTION    433 

7.  In  what  sense  can  it  be  said  that  scientific  explanation 
is  a  process  by  which  what  is  given  in  observation  is 
supplemented  by  what  is  not  so  given? 

8.  Can  you  connect  the  conception  of  scientific  explanation 
implied  in  the  previous  question  with  the  conception  of 
knowledge  stated  in  Chapter  I? 

9.  State   and   illustrate  three   senses   in  which   the   word 
analogy  is  used. 

10.  Why  is  not  any  kind  or  degree  of  resemblance  a  safe 
principle  of  inference? 

11.  What  is  meant  when  it  is  said  that  analogical  reasoning 
depends  upon  important  resemblances?  . 

12.  In  what  way  does  the  validity  of  reasoning  by  analogy 
depend  upon  the  attitude  one  takes  toward  differences? 

13.  What  light  does  the  saying  that  analogy  'sticks  in  the 
particular  instances'  throw  upon  the  character  of  ana- 
logical argument? 

14.  In  what  sense  can  analogy  be  regarded  as  a  method  of 
explanation  ? 

15.  What  are  the  limits  of  analogical  argument? 

16.  What  does  Mill  mean  by  calling  analogy  'a  mere  sign 
post'? 

17.  State  and  illustrate  what  you  understand  by  an  hypoth- 
esis. 

18.  Why  must  hypotheses  be  stated  in  terms  of  the  same 
order  as  the  phenomena  they  attempt  to  explain? 

19.  Is    there     any    objection     against    calling    hypotheses 
'guesses,'  and,  if  so,  what  is  the  ground  on  which  it 
rests? 

20.  What  reason  may  be  given  for  the  scientists'  objection 
to  the  use  of  hypotheses? 

21.  What  is  the  relation  of  imagination  to  the  task  of  for- 
mulating scientific   hypotheses? 

22.  What   are   some  of  the   'facts'  which  we   owe   to   the 
exercise    of   imagination    in    the    field    of   the    natural 
sciences? 

38 


434  A  TEXT-BOOK  OF  LOGIC 

23.  State  and  explain  the  two  steps  involved  in  the  veri- 
fication of  hypotheses? 

24.  Illustrate  by  the  use  of  concrete  example  the  process 
of  verifying  an  hypothesis. 

25.  How   do  hypothesis  and  theory  agree  with   and  differ 
from  each  other?     Illustrate. 

EXERCISES 

1.  Examine  the  explanations  of  three  simple  events  with 
which  you  are  acquainted,  and  state  whether  they  con- 
form or  not  to  the  fundamental   form  of  explanation 
as  stated  in  the  text. 

2.  Give  three  instances  in  which  explanation  consists  in  the 
statement  of  the  conditions   of  a  phenomenon's  occur- 
rence. 

3.  Give  two  llustrations,  one  from  literature  and  one  from 
science,  of  analogy.    Examine  each  with  a  view  to  show- 
ing to   which  meaning  of  the  word   it  conforms,   and 
whether  it  satisfies  the  conditions  of  a  valid  inference. 

4.  Upon  what  logical  principle  does  each  of  the  following 
statements  depend,  and  what  can  you  say  as  to  their 
validity  as  arguments: 

(1)  It  is  said  that  a  general  resemblance  of  the  hills 
near    Ballarat    in    Australia    to    the    California    hills 

where  gold  had  been  found  suggested  the  idea  of 
digging  for  gold  at  Ballarat. 

(2)  There  are  no  great  nations  of  antiquity  but  have 
fallen  to  the  hand  of  time;  and  England  must  join 
them  to  complete  the  analogy  of  the  ages.     Like 
them  she  has  grown  from  a  birth-time  of  weakness 
tutelage  to  a  day  of  manhood  and  supremacy,  but 
she    has    to    face    her    setting.      Everything    that 
grows  must  also  decay. 

5.  Construct  an  hypothesis  to  explain  some  fact  of  your 
experience,  and  explain  how  it  may  be  verified  or  over- 
thrown. 


CHAPTER  XVI 

CAUSATION 

General  Statement  of  the  Problem.  The  fact  that 
underlies  the  problem  of  causation  is  the  observed 
regularity  in  the  order  of  the  particular  phenomena 
which  occur  in  the  course  of  our  ordinary  expe- 
rience, and  in  the  fields  of  the  several  sciences. 
That  our  ordinary  and  scientific  experience  is  char- 
acterised, within  ascertainable  limits,  by  some  kinds 
and  degrees  of  regularity  is  a  fact  about  which 
there  is  universal  agreement.  Indeed,  this  is  a  fea- 
ture of  experience  so  generally  recognised  that  it 
constitutes  the  starting  point  not  only  of  the  theo- 
retical interest  which  leads  us  to  the  more  accurate 
forms  of  human  knowledge,  but  also  of  the  practical 
interests  which  lie  at  the  foundation  of  the  political, 
commercial,  and  social  relations  by  which  human 
individuals  are  held  together  in  a  community.  A 
world  from  which  all  order  were  absent  would  be  a 
world  in  which  all  thought  and  action  would  be  im- 
possible, and  to  which  all  thinking  and  active  agents 
would  ultimately  succumb.  The  institutions  of 
society  and  the  organisation  of  the  sciences  pre- 
supposes that  some  sort  of  unity  and  order  belong 
to  the  world ;  and  it  is  the  business  of  all  our  sciences 
to  study  the  regularities  of  the  phenomena  and 
events  of  the  world  for  the  purpose  of  endowing 
our  notion  of  such  regularities  with  greater  pre- 

(435) 


436  A  TEXT-BOOK  OF  LOGIC 

cision.  The  problem,  then,  that  confronts  us  in  view 
of  this  regularity  of  the  world's  order  is :  How  shall 
we  conceive  this  regularity  so  as  to  make  intelligible 
to  ourselves  the  principles  or  laws  by  which  it  is 
maintained  and  upon  which  it  depends? 

The  Practical  Aspect  of  the  Question.  There  is 
no  doubt  that  this  is  not  a  theoretical  question 
merely,  a  question  only  of  the  sciences,  and  unim- 
portant or  superfluous  in  the  absence  of  theoretical 
interests.  The  way  in  which  the  world  in  which 
we  live  may  be  expected  to  behave  is  a  broadly 
practical  interest;  and  the  man  who  in  the  morning 
starts  off  to  his  office,  as  well  as  the  one  who  goes  to 
his  laboratory,  begins  the  day's  work  with  the  ex- 
pectation that  the  uniformities  upon  which  he  has 
relied  in  the  past  will  be  maintained  in  the  present. 
Indeed,  we  may  say  that,  in  the  history  of  the  indi- 
vidual and  of  the  race,  interest  in  the  regularity 
of  the  course  of  observed  events  was  practical  before 
it  was  theoretical;  and  it  would  not  be  difficult  to 
show  that  the  practical  motive  has  never  been 
divorced  from  the  theoretical  when,  in  the  progress 
of  the  sciences,  these  uniformities  have  become 
the  subject  of  very  specialised  study.  No  one, 
for  instance,  who  has  the  least  knowledge  of 
primitive  peoples  can  fail  to  be  impressed  with  the 
fact  that  the  origin  and  development  of  their  insti- 
tutions is  closely  interwoven  with  their  struggle 
with  the  forces  of  nature.  Upon  his  understanding 
of  the  physical  world  has  depended  the  primitive 
man's  ability  to  maintain  himself  in  existence.  We 


CAUSATION  437 

see  the  relationship  thus  indicated  between  the 
growth  of  intelligence  and  the  economic  struggle 
illustrated  in  a  broad  way  if  we  contrast,  for  ex- 
ample, the  peoples  of  the  northern  and  southern 
latitudes.  Whenever,  as  in  the  latter  case,  the  food 
supply  is  plentiful  and  relatively  independent  of  the 
cultivation  of  the  domestic  arts,  intelligence  is  com- 
paratively low ;  but  when,  as  in  the  former  case,  the 
food  supply  is  scanty  or  precarious,  it  becomes 
increasingly  important  to  understand  the  physical 
environment  from  which  has  to  be  won  the  means 
of  physical  support,  and,  if  the  community  is  to 
perpetuate  itself,  to  socialise  this  knowledge  in  the 
domestic  arts. 

There  are  many  concrete  illustrations  of  the 
way  in  which,  at  the  present  time,  observation 
of  natural  occurrences,  and  inferences  drawn  from 
such  observation,  are  allowed  to  affect  our  prac- 
tical life.  From  the  character  of  the  sunset 
we  infer  that  it  will  be  a  fair  or  stormy  day  to- 
morrow, and,  therefore,  that  it  will,  or  will  not,  be 
possible  to  take  a  day's  outing  in  the  country.  What 
the  farmer  calls  'good  growing  weather'  is  an  infer- 
ence, based  upon  observed  connections  in  the  past, 
of  the  same  practical  sort.  Now  about  the  facts  that 
underlie  such  practical  inferences  as  these,  we  may 
observe  that  they  are  selected,  often  by  the  cooper- 
ative labours  of  many  generations  of  observant  men, 
from  a  very  complex  mass  of  details,  and  that  no 
effort  is  made,  as  a  rule,  either  to  determine  the  pre- 
cise nature  and  connection  of  the  facts  themselves, 


438  A   TEXT-BOOK   OF  LOGIC 

or  to  enumerate  exhaustively  the  other  factors  with 
which,  in  our  experience,  they  are  associated.  For 
example,  what  constitutes  'good  growing  weather' 
may  be  for  one  man  a  matter  of  temperature,  for 
another  a  matter  of  humidity,  and  for  a  third  a 
matter  of  both ;  but  neither  of  these  factors,  nor  both 
together,  can  be  regarded  as  a  sufficient  explanation 
of  the  term,  and  many  other  elements  of  the  situ- 
ation in  which  it  is  relevant  to  talk  about  growing 
weather  must  be  taken  account  of  —  such,  for  in- 
stance, as  the  nature  of  the  particular  crop,  the 
particular  stage  of  its  growth,  its  condition  at  that 
stage,  the  nature  of  the  soil,  the  location  of  the  field 
in  which  the  crop  is  growing,  etc.  —  if  the  phrase 
is  to  have  for  us  any  practical  significance.  When, 
therefore,  we  examine  the  character  of  those  uni- 
formities which  our  practical  interests  lead  us  to 
observe,  we  find  that  they  are  made  up  of  certain 
striking  or  important  features  of  a  complex  situ- 
ation, which  are  connected  together  in  such  a  way 
that,  on  their  recurrence  in  our  experience,  we  are 
led  to  expect  the  recurrence  of  other  features  of  the 
situation  with  which  they  have  been  associated  in 
our  past  experience.  In  other  words,  one  part  of 
an  experience  is  taken  as  a  sign  of  the  recurrence 
of  another  part  with  which  it  is  usually  connected. 
Beyond  such  empirical  connections  as  are  found  in 
experience,  the  practical  view  of  causation  does  not 
enable  us  to  advance. 

The  Theoretical  Aspect  of  the  Question.       If    we 
compare  the  theoretical  with  the  practical  way  of 


CAUSATION  439 

dealing  with  the  observed  regularities  in  the  occur- 
rence of  natural  events,  we  shall  see  that  it  differs 
from  the  latter  in  two  respects.  In  the  first  place, 
the  theoretical  view,  in  Venn's  suggestive  phrase, 
'screws  up'  the  antecedent  or  cause  and  the  conse- 
quent or  effect  of  an  event  into  close  juxtaposition, 
so  that  they  come  to  be  regarded  as  nearly  as  pos- 
sible concurrent.  The  possibility  of  doing  this,  it  is 
obvious,  depends  upon  our  ability  to  eliminate  from 
the  phenomenon  we  are  examining  all  the  disturb- 
ing or  irrelevant  elements.  If,  therefore,  it  is  re- 
membered that  no  two  natural  events  are  exactly 
alike  in  all  their  details,  that  some  of  the  attendant 
circumstances  are  peculiar  to  the  instance  of  the 
phenomenon  we  are  examining,  and  form  no  part  of 
the  phenomenon  itself,  it  is  evident  that  the  omission 
of  these,  by  whatever  means  it  is  brought  about, 
can  serve  only  to  give  greater  precision  to  the  fac- 
tors that  are  involved  in  the  orderly  sequence,  and 
to  make  it  possible  to  determine  with  greater  accu- 
racy the  details  which  are  involved  in  the  causal 
relation.  We  pass  from  the  practical  to  the  more 
theoretical  view  of  causation,  that  is  to  say,  when 
we  devise  means  of  eliminating  from  our  observa- 
tion of  natural  events  what  is  irrelevant  to  our. 
search  for  the  conditions  of  the  occurrence  of  such 
events. 

In  the  second  place,  the  theoretical  view  insists 
upon  the  importance  of  a  careful  analysis  of  the 
antecedents  of  an  event  as  a  condition  of  establish- 
ing a  causal  relation.  Mill  insisted  on  this  point 


440  A  TEXT-BOOK  OF  LOGIC 

with  some  emphasis,  and  he  criticised  the  practical 
view  for  the  unregulated  way  in  which  it  picks  out 
some  one  event  or  circumstance,  and  calls  it  the 
cause.  There  is  just  ground  for  Mill's  contention, 
if  our  study  of  the  observed  regularities  in  the 
occurrences  of  natural  phenomena  is  made  from 
the  point  of  view  of  the  requirements  of  accu- 
rate knowledge;  but  if  we  admit  the  legitimacy  of 
the  practical  point  of  view,  if,  that  is,  the  order  of 
nature's  changes  are  taken  as  a  clue  to  the  kinds  of 
conduct  that  are  likely  to  be  efficient,  we  may  say 
that  the  more  refined  analysis  that  Mill  had  in  mind, 
and  which  is  required  by  science,  would  in  large 
measure  defeat  this  latter  purpose.  It  is  because 
the  interests  of  science  are  so  intimately  bound  up 
with  a  detailed  knowledge  of  the  conditions  of  phe- 
nominal  occurrences  that,  in  contrast  with  those  of 
the  practical  life,  its  requirements  are  satisfied  only 
by  the  minute  analysis  of  the  phenomena  with  which 
it  is  particularly  concerned.  In  emphasising  this 
point  Mill  has  directed  attention  to  an  important 
difference  between  the  practical  and  theoretical 
views  of  the  causal  relation. 

The  Genetic  Relation  of  the  Practical  and  Theo- 
retical Views.  While  the  theoretical  view  of  caus- 
ation differs,  as  we  have  said,  from  the  practical  in 
important  respects,  we  should  be  departing  from 
the  truth  if  we  supposed  that  the  differences  between 
these  views  expressed  the  whole  truth  about  them. 
There  is  between  the  two  views  no  such  opposition 
in  fact  as  an  examination  of  their  differences  alone 


CAUSATION  441 

would  lead  one  to  think.  We  must  regard  them, 
rather,  as  earlier  and  later  stages  in  the  progressive 
efforts  of  the  race  to  make  clear  to  itself  the  rela- 
tion in  which  it  stands  to  the  changing  environment 
under  which  its  life  has  to  be  lived.  It  was  doubt- 
less useful  for  the  theoretical  view  that  practical 
interests  had  led  to  the  observation  of  large  numbers 
of  uniformity  in  the  occurrence  of  natural  events. 
In  this  way,  material  was  already  prepared  for  it, 
and  to  this  material  it  could  apply  the  stricter 
methods  which  a  change  in  interests  was  the  means 
of  defining.  But  in  developing  and  applying  these 
methods  the  sciences  have  not  freed  themselves  alto- 
gether from  practical  considerations  and,  moreover, 
have  themselves  contributed  very  largely  toward  a 
new  and  broader  conception  of  the  practical  itself. 
By  this  statement  we  do  not  merely  mean  that,  in  its 
history,  scientific  progress  frequently  has  been 
determined  by  difficulties  encountered  in  a  narrowly 
practical  way,  nor  merely  that  scientific  truth  has 
so  often  been  found  capable  of  a  like  practical 
application;  the  more  important  fact  is  that,  as 
scientific  aims  and  methods  have  become  established, 
our  conception  of  what  is  practical  has  been  broad- 
ened to  include  any  kind  of  activity  that  is  directed 
toward  the  attainment  of  an  end.  In  the  sense  in 
which  nowadays  we  use  the  word,  any  regulated  or 
consciously  controlled  process  is  practical,  and  it 
would  seem  that  science  has  not  only  contributed  to 
this  conception  but  is  itself,  in  this  meaning  of  the 
term,  preeminently  a  practical  affair.  And  just  be- 


442  A  TEXT-BOOK   OF  LOGIC 

cause  the  scientific  man  approaches  his  problems 
with  definite  questions  in  his  mind,  because,  as 
Bacon  said,  he  interrogates  nature,  there  is  a  limit 
set,  by  the  nature  of  the  questions  themselves,  to 
the  amount  of  analysis  that  is  necessary  in  arriving 
at  the  solution  of  particular  problems.  It  is  not, 
therefore,  in  the  amount  of  analysis  performed  that 
we  can  find  the  distinguishing  mark  of  a  theoretical 
view  of  the  causal  question.  For  if  we  insist  that 
our  analysis  in  any  field  whatever  must  be  relevant, 
in  kind  and  amount,  to  the  purpose  for  which  it  is 
undertaken,  it  becomes  at  once  obvious  that  the 
practical  and  theoretical  views  are  brought  together 
under  a  single  view,  and  that  the  differences  enu- 
merated above  must  be  understood,  not  as  placing 
the  views  in  question  in  different  classes,  but  as  indi- 
cating different  species  of  activity  which  belong  to  a 
single  class. 

The  Origin  and  Nature  of  the  Causal  Problem. 
In  view  of  the  foregoing  considerations,  two  facts 
may  be  said  to  be  fairly  well  established.  In  the 
first  place,  there  is  good  reason  for  believing  that 
the  causal  problem  arises  from  the  importance  that 
the  presence  of  order  in  human  experience  has  for 
the  practical  no  less  than  for  the  theoretical  life. 
The  problem  of  causation  is  of  such  general  interest, 
as  we  have  seen,  not  because  the  world  in  which 
we  live  is  unregulated  and  disordered,  but  because, 
being  regulated  and-  ordered,  we  can  adjust  our- 
selves to  it  better  if  we  know  the  principles  and 
laws  according  to  which,  in  the  future  as  in  the 


CAUSATION  443 

past,  things  and  events  may  be  expected  to  happen. 
It  is  well  to  be  perfectly  clear  on  this  point,  because 
frequently  its  neglect  has  led  to  a  somewhat  one- 
sided, if  not  misleading,  view  of  the  problem  itself. 
We  have  called  attention  to  the  impossibility  of 
considering  the  causal  problem  as  in  any  essential 
respect  different  for  the  scientist  than  for  the  prac- 
tical man.  For  both,  it  is  the  fact  that  experience 
presents  us  with  certain  regularities  in  the  order 
of  our  experience  that  directs  attention  to  the  prob- 
lem, and  that  leads  to  a  study  of  these  regularities. 
We  do  not  study  the  causal  problem,  that  is  to  say, 
to  escape  from  a  world  of  chaos  to  a  world  of  order, 
but,  starting  with  the  world  of  order,  we  seek  to 
understand  its  laws,  and  to  ascertain  how  far  these 
laws  are  capable  of  being  extended  to  new  and 
larger  areas  of  life. 

In  the  second  place,  it  is  clear  that  the  problem 
of  causation  has  nothing  whatever  to  do  with  the 
question  why  things  happen  as  they  do,  if  by  that 
question  is  meant  an  inquiry  into  the  reasons  why 
our  experience  has  the  distinctive  characteristics 
that  it  is  known  to  have.  Science,  and  the  same 
thing  is  equally  true  of  philosophy,  starts  with  the 
acceptance  of  the  world  as  it  is  known  in  human 
experience,  a  world,  as  we  have  seen,  that  has  a  cer- 
tain determinate  character.  Now  about  such  a  world, 
it  would  be  futile  to  ask  ourselves  why  it  has  this 
rather  than  some  other  character,  since  the  very 
problems  which  confront  us  in  our  everyday  life,  and 
in  our  sciences  and  philosophy  as  well,  arise  out 


444  A  TEXT-BOOK  OF  LOGIC 

of  the  world's  character  as  made  known  by  human 
observation.  The  facts  about  the  world  in  which 
we  live,  as  these  are  observed  and  reported  in  in- 
creasing numbers  and  with  improving  accuracy, 
constitute  the  material  of  all  human  knowledge,  and 
if  there  are  any  further  questions  that  arise,  these 
must  concern  the  way  in  which  such  facts  are  con- 
nected in  the  unity  of  an  ordered  system.  Instead, 
therefore,  of  conceiving  the  causal  problem  as  an 
inquiry  into  the  reason  why  facts  are  what  they 
are,  we  must  view  it  rather  as  demanding  of  us  an 
exposition  of  the  nature  of  the  connection  that  binds 
the  various  parts  of  human  experience  together. 
Put  simply,  the  causal  problem  is  concerned,  not 
with  the  question  why  things  are  what  they  are, 
but  with  the  question  how  things  happen  as  they 
do. 

The  Course  of  Our  Further  Discussion.  Our  fur- 
ther study  of  the  causal  problem  will  bring  before 
us  particularly  three  closely  related  questions.  We 
shall  examine,  in  the  first  place,  the  time  relations 
of  causal  events;  in  the  second  place,  the  complex 
character  of  such  events  will  demand  attention; 
and  in  the  third  place,  we  must  try  to  make  clear 
what  is  meant  by  the  necessity  that  is  always  recog- 
nised as  belonging  to  such  events.  In  our  discussion 
of  each  of  these  topics,  we  shall  make  Mill's  'treat- 
ment, in  Book  III.,  Chapter  V.,  of  the  Logic,  our 
point  of  departure.  It  will  be  advantageous,  there- 
fore, for  the  student  to  read  the  whole  of  Mill's 


CAUSATION  445 

chapter   in   connection    with   the   following   para- 
graphs. 

The  Time  Relations  of  Causal  Events.  The  first 
characteristic  of  a  causal  relation  that  Mill  enu- 
merates is  the  'invariable  antecedence'  of  certain  of 
the  factors  involved  in  the  causal  relation.  He  says 
that  "invariability  of  succession  is  found  by  observa- 
tion to  obtain  between  every  fact  in  nature  and 
some  other  fact  which  preceded  it.  ...  The 
invariable  antecedent  is  termed  the  cause;  the  in- 
variable consequent,  the  effect.  And  the  universal 
law  of  causation  consists  in  this,  that  every  conse- 
quent is  connected  in  this  manner  with  some  ante- 
cedent or  set  of  antecedents.  .  .  .  For  every  event 
there  exists  some  combination  of  objects  or  events, 
some  given  concurrence  of  circumstances,  positive 
and  negative,  the  occurrence  of  which  is  always 
followed  by  that  phenomenon."  He  points  out  that 
we  may  not  have  discovered  what  the  particular 
concurrence  of  circumstances  may  be  in  a  given 
case,  "but,"  he  adds,  "we  never  doubt  that  there  is 
such  a  one,  and  that  it  never  occurs  without  having 
the  phenomenon  in  question  as  its  effect  or  conse- 
quence." 

In  this  passage,  Mill  definitely  raises  the  ques- 
tion of  the  time  relations  of  causal  events.  In  lay- 
ing emphasis  on  the  antecedence  of  the  cause,  Mill 
takes  the  view  that  for  any  event  to  be  considered 
as  a  cause  at  all,  it  must  exist  in  time  before  the 
event  which  is,  or  may  be  regarded  as,  its  effect. 
This,  doubtless,  is  the  conception  of  the  time  rela- 


446  A  TEXT-BOOK  OF  LOGIC 

tions  of  cause  and  effect  that  prevails  generally  at 
the  present  day,  and  it  may  be  worth  while  to  ask 
how  far  it  is  an  accurate  description  of  the  facts 
that  are  involved  in  causal  events.  There  are, 
without  question,  many  examples  of  the  causal  rela- 
tion that  lend  themselves  quite  naturally  and  easily 
to  this  interpretation,  examples,  that  is  to  say,  in 
which  the  fact  that  we  call  the  cause  and  the  fact 
that  we  call  the  effect  appear  to  be  temporally  dis- 
tinct events.  A  blow  on  the  head,  for  instance,  may 
be  followed  by  the  loss  of  consciousness,  and 
may  be  said  to  be  the  cause  of  the  loss  of  con- 
sciousness. The  explosion  of  a  powder  magazine 
may  follow  the  application  of  a  lighted  match  or 
fuse  to  the  powder.  Diphtheria  makes  its  appear- 
ance ten  days  after  the  ingestion  of  the  Klebs- 
Loeffler  bacillus  which,  the  physicians  tell  us,  is  the 
cause  of  the  disease.  In  all  these  cases  we  have,  or 
seem  to  have,  undoubted  examples  of  the  necessary 
temporal  priority  of  the  cause,  and  the  necessary 
posteriority  of  the  effect,  in  causally  related  phe- 
nomena. It  may  be  doubted,  however,  whether  all 
causally  related  events  can  be  made  to  fall  so  easily 
and  naturally  within  this  scheme  or  view.  It  would 
be  difficult,  for  example,  to  detect  in  the  explanation 
offered  by  the  chemist  of  the  formation  of  rust  the 
temporal  discontinuity  of  cause  and  effect  which  is 
an  essential  part  of  Mill's  doctrine  of  causation. 
Rust  formation,  so  we  are  told,  is  due  to  the  combi- 
nation of  iron  with  the  free  oxygen  of  the  air;  but, 
if  that  is  so,  it  is  quite  obvious  that  the  chemical 


CAUSATION  447 

combination  of  oxygen  and  iron  does  not  precede, 
but  is  contemporaneous  with,  the  formation  of  rust 
itself.  There  are  innumerable  instances  of  a  similar 
character,  and  we  may  even  say  that  the  example 
chosen  is  typical  of  most  of  the  chemical  processes 
with  which  we  are  at  all  familiar.  The  case  is  im- 
portant because  of  the  large  field  of  application  of 
chemical  laws,  not  only  in  the  inorganic,  but  in  the 
organic  world  as  well.  To  take  only  one  such 
example,  we  now  know  that  bacterial  action  is 
largely,  if  not  wholly,  due  to  the  toxins  generated 
by  microscopic  organisms;  and,  if  that  is  true,  the 
final  explanation  of  their  action  and  results  is,  as 
is  coming  to  be  seen,  a  highly  specialised  branch  of 
the  science  of  chemistry.  If,  as  seems  probable,  the 
results  of  bacterial  action  are  not  separable  in  time 
from  the  production  of  their  toxins,  an  overwhelm- 
ing list  of  examples  can  be  appealed  to  to  throw 
doubt  on  the  necessary  temporal  antecedence  and 
consequence  of  the  events  involved  in  the  causal 
relation. 

It  is  owing  to  some  such  considerations  as  these 
that  the  position  has  sometimes  been  taken  that 
there  is  no  distinction  whatever  between  the  cause 
and  the  effect  of  a  phenomenon,  in  other  words, 
that  the  cause  and  effect  are  identical.  There  seems 
no  sufficient  reason  in  the  nature  of  causal  phe- 
nomena why  we  should  adopt  so  paradoxical  a  view. 
Cause  and  effect  do  stand  for  distinct  things  in  our 
experience  of  causal  events,  and  if,  as  we  have  said, 
this  distinction  is  not  necessarily  one  of  temporal 


448  A  TEXT-BOOK  OF  LOGIC 

discontinuity,  we  need  to  inquire  further  what  the 
distinction  is. 

When  we  say  that  the  relation  of  cause  and 
effect  is  not  necessarily  one  of  antecedence  and 
consequence  in  time,  we  must  not  be  understood  to 
affirm  that  causal  phenomena  have  no  relation  at 
all  to  time.  That  would  be  not  only  a  paradox,  but 
exceedingly  difficult  to  maintain.  It  is  no  doubt 
true  that  all  causal  phenomena  are  events  in  time, 
that  they  are  constituted  by  a  number  of  facts 
which  come  before  and  after  one  another  in  a  series. 
That  the  whole  number  of  facts  in  a  causal  phe- 
nomenon have  a  definite  sequence  and  order  in  time 
there  is  no  need  to  deny,  and  that  the  order  and 
sequence  can  be  determined  is  the  permanent  ex- 
pectation and  belief  of  science.  From  this  fact, 
however,  it  does  not  follow  that,  within  the  series, 
the  cause  and  effect  are  separated  by  a  necessary  tem- 
poral interval.  What  rather  we  seem  warranted 
in  saying  with  respect  to  the  causal  series  is  that 
their  factors  are  continuous,  —  temporal  continuity, 
not  temporal  discontinuity,  seems  to  be  the  charac- 
teristic of  all  such  events.  But  whether  within  the 
causal  series  the  cause  antedates  the  effect,  or  is 
contemporaneous,  at  least  in  part,  with  it,  as  it 
must  be,  for  example,  in  the  circular  reactions  of 
chemistry,  is  a  fact  to  be  determined  in  the  par- 
ticular instance.  But  whatever  may  be  true  of  any 
particular  instance,  temporal  discontinunity  cannot 
be  regarded  as  an  essential  feature  of  the  causal 
relation.  The  utmost  that  we  can  say,  from  the 


CAUSATION  449 

standpoint  of  their  temporal  relations,  is  that  the 
cause  and  effect  are  continuous  with  one  another. 

The  Complex  Character  of  Causal  Events.  It  is 
seldom,  if  ever,  according  to  Mill,  that  an  invariable 
sequence  subsists  between  a  consequent  and  a  single 
antecedent.  Usually,  the  causal  relation  exists 
between  "a  consequent  and  the  sum  of  several  ante- 
cedents ;  the  concurrence  of  all  of  them  being  requi- 
site to  produce,  that  is,  to  be  certain  of  being  fol- 
lowed by,  the  consequent."  If,  for  example,  "a  per- 
son eats  of  a  particular  dish  and  dies  in  consequence, 
that  is,  would  not  have  died  if  he  had  not  eaten  of 
it,"  the  death  is  usually  attributed  to  eating  of  the 
dish  although,  as  Mill  points  out,  there  were  other 
factors  contributing  to  the  result,  such  as  the  bodily 
constitution  of  the  individual,  the  particular  state 
of  his  health,  and,  perhaps,  a  certain  state  of  the 
atmosphere.  These  taken  in  conjunction  with  eat- 
ing of  the  dish  are,  according  to  Mill's  view,  the 
'invariable  antecedent/  When  we  select  one  among 
the  antecedents  of  a  phenomenon  and  call  this  the 
cause,  our  selection,  Mill  says,  falls  generally  on 
the  one  which  came  last  into  existence.  But,  he  also 
points  out,  there  is  hardly  any  one  among  the  num- 
ber of  antecedents  that  may  not  serve  in  this  special 
sense  as  the  cause  "according  to  the  purpose  of  our 
immediate  discourse."  This  tendency  "to  associate 
the  idea  of  causation  with  the  proximate  antece- 
dent event,  rather  than  with  any  of  the  antecedent 
states,  or  permanent  facts,  which  may  happen  also 


450  A  TEXT-BOOK  OF  LOGIC 


to  be  conditions  of  the  phenomenon,"  Mill  regards 
as  not  at  all  necessary  to  the  common  notion  of 
cause.  The  conclusion,  then,  at  which  he  arrives 
is  that  by  a  cause  is  meant  "the  sum  total  of  the 
conditions,  positive  and  negative,  taken  together; 
the  whole  of  the  contingencies  of  every  description 
which  being  realised,  the  consequent  invariably  fol- 
lows. The  negative  conditions  .  .  .  may  be  all 
summed  up  under  one  head,  namely,  the  absence 
of  preventing  or  counteracting  causes." 

The  essential  contentions  of  Mill  in  this  passage 
are,  first,  that  the  antecedent  of  any  fact  is  a  com- 
plex group  of  facts,  and,  second,  that  the  cause, 
popularly  considered,  is  taken  to  be  some  one  fact 
among  the  antecedents  selected  arbitrarily  or  for 
some  special  purpose.  With  regard  to  the  first 
point  we  may  quote  Jevons.  He  says :  "By  an  ante- 
cedent we  mean  any  thing,  condition,  or  circum- 
stance which  exists  before  or,  it  may  be,  at  the  same 
time  with  an  event  or  phenomenon.  By  a  conse- 
quent we  mean  any  thing,  circumstance,  event,  or 
phenomenon,  which  is  different  from  any  of  the 
antecedents  and  follows  after  their  conjunction  or 
putting  together.  It  does  not  follow  that  an  ante- 
cedent is  a  cause,  for  the  effect  might  have  hap- 
pened without  it.  Thus  the  sun's  light  may  be  an 
antecedent  to  the  burning  of  a  house,  but  not  the 
cause,  because  the  house  would  burn  equally  well 
in  the  night;  but  a  necessary  or  indispensable  ante- 
cedent is  identical  with  a  cause,  being  that  without 
which  the  event  would  not  take  place.  .  .  .  There 


CAUSATION  451 

are  usually  many  different  things,  conditions,  or 
circumstances  necessary  to  the  production  of  an 
effect,  and  all  of  them  must  be  considered  causes 
or  necessary  parts  of  the  cause.  Thus  the  cause 
of  the  loud  explosion  in  a  gun  is  not  simply  the 
pulling  of  the  trigger,  which  is  only  the  last  appar- 
ent cause  or  occasion  of  the  explosion ;  the  qualities 
of  the  powder,  the  proper  form  of  the  barrel,  the 
proper  arrangement  of  the  percussion-cap  and  pow- 
der, the  existence  of  the  surrounding  atmosphere, 
are  among  the  circumstances  necessary  to  the  loud 
report  of  a  gun ;  any  of  them  being  absent  it  would 
not  have  occurred."  In  this  passage  it  may  be 
observed  that  what  is  popularly  regarded  as  the 
cause,  the  second  point  mentioned  by  Mill,  Jevons 
calls  the  occasion  of  the  event,  that  is,  that  which, 
in  connection  with  the  other  necessary  antecedent 
or  coexisting  conditions,  is  effective  in  bringing 
these  latter  into  active  operation.  What  Jevons 
here  speaks  of  as  the  occasion  is  sometimes  called 
the  immediate  cause,  the  other  necessary  attendant 
circumstances  being  referred  to  as  the  conditions 
or  causal  conditions  of  the  event  in  question. 

That  the  cause  of  any  event  is  some  complex 
group  of  facts  or  circumstances  is  undoubtedly  true. 
Indeed,  this  seems  to  follow  as  a  matter  of  necessity 
from  the  general  character  of  human  experience. 
As  we  have  pointed  out  frequently,  objects  and 
events  are  experienced  by  us,  not  as  separate  and 
individual  things,  but  as  subsisting  with  other  ob- 
jects and  events  with  which  they  are  connected  in 


452  A  TEXT-BOOK  OF  LOGIC 

a  variety  of  ways.  It  is  this  feature  of  experience 
that  was  said  above  to  be  the  starting  point  of  the 
casual  problem.  Now  it  is  no  doubt  true  that  within 
any  experienced  complex  we  can,  and  in  fact  do, 
isolate,  by  an  act  of  discriminative  attention,  a 
given  fact  or  event  which  we  regard,  for  reasons 
special  to  the  case,  as  the  effect  or  result  of  other 
perceived  or  discoverable  facts,  and  that,  in  this 
way,  a  certain  uniqueness,  a  certain  independence, 
comes  to  be  regarded  as  the  distinguishing  mark  of 
all  effects  whatever.  But  while  no  objection  can  be 
brought  against  thus  isolating  an  effect,  since  in  this 
way  it  is  rendered  more  capable  of  exact  descrip- 
tion, and  the  particular  causal  relation  that  has  to 
be  determined  is  made  more  capable  of  exact  defi- 
nition, a  similar  line  of  remark  does  not  apply  to 
what  we  understand  as  a  cause.  For,  in  the  first 
place,  it  is  only  because  what  we  call  the  effect 
has  a  definite  character  that  the  search  for  a  cause 
becomes  a  problem  at  all.  Unless  the  fact  or  event 
of  which  we  wished  an  explanation  were  made 
definite,  there  would  be  no  point  of  starting  for  the 
establishment  of  a  causal  relation.  It  is  owing  to 
the  fact  that  some  part  of  the  experience  of  which 
the  effect  is  only  a  fragment  remains  indefinite  that 
the  cause  is  characterised  at  first  by  an  indeter- 
minateness  that  would  be  quite  fatal  if  it  attached 
to  the  effect. 

But,  not  to  press  this  point,  we  cannot  be 
sure,  in  the  second  place,  that,  in  any  particular 
case,  all  the  conditions  which  will  make  the  oc- 


CAUSATION  453 

currence  of  an  effect  intelligible  fall  within  our 
experience  of  that  case.  As  we  have  seen  above, 
experimental  and  theoretical  observation  are  val- 
uable chiefly  because  they  bring  within  experience 
factors,  material  to  our  understanding  of  a  phe- 
nomenon, that  are  not  included  in  our  ordinary 
perception  of  it.  An  example,  usually  cited,  is  the 
discovery  of  the  planet  Neptune  by  Galileo  in  1846. 
The  observed  fact  which  led  to  its  discovery  was  the 
deviation  of  the  planet  Uranus  from  the  course 
determined  for  it  by  the  attractive  forces  of  the 
sun,  Jupiter,  and  Saturn.  It  was  suggested,  first 
by  Adams  and  later  by  LeVerrier,  that  this  devia- 
tion could  be  accounted  for  if  we  supposed  that 
some  hitherto  unknown  body,  situated  external  to 
it  in  a  particular  position  and  at  a  given  distance, 
were  affecting  the  movement  of  the  planet.  Such 
a  body,  situated  where  Adams  and  LeVerrier  had 
suggested,  was  later  discovered  by  Galileo,  and 
exists  in  our  solar  system  as  the  planet  Neptune. 
In  the  third  place,  we  may  observe  that,  whether 
all  the  factors  necessary  to  a  causal  relation  are  or 
are  not  parts  of  our  ordinary  perception  of  it,  as 
indeed  the  illustration  just  used  is  sufficient  to  show, 
the  effectiveness  of  any  given  fact,  —  the  planet 
Neptune,  for  example,  —  seems  to  depend  as  much 
on  its  relations  to  other  facts,  —  the  sun,  Jupiter 
and  Saturn,  —  as  it  does  on  its  own  existence.  It 
is  no  doubt  true  that  if  the  fact,  —  the  planet  Nep- 
tune, —  did  not  exist,  it  could  be  neither  a  cause 
nor  any  part  of  a  cause ;  but  if  it  is  a  cause  or  part 


454  A  TEXT-BOOK  OF  LOGIC 

of  a  cause  at  all,  it  owes  this  character,  not  merely 
to  its  existence,  but  also  to  the  way  it  acts  and  is 
acted  upon  by  other  facts  in  the  system  of  facts  in 
which  the  effect,  —  the  course  of  Uranus,  —  is  in- 
cluded as  an  important,  and,  indeed,  a  necessary  ele- 
ment. To  take  another  illustration,  we  cannot  re- 
gard death  as  the  result  of  a  gun  shot,  poison,  or 
any  other  single  fact,  but  as  the  result  of  a  net- 
work of  facts  which  includes  the  gun  shot  or  what 
not  in  a  system  which  extends  to  and  embraces  the 
stated  effect.  From  this  point  of  view,  it  is  evident 
that  the  problem  of  causation  is  one  in  which,  start- 
ing with  some  fact  or  event,  we  endeavour  to  build 
up  by  observation  and  experiment  a  system  of  facts 
within  which  the  fact  or  event  with  which  we 
started  is  necessarily  included.  Causes,  conse- 
quently, must  always  be  complex,  and  the  difficulty 
of  determining  causes  is  the  difficulty  of  including 
within  the  system  only  those  factors  that  are  mate- 
rial to  it. 

Few  words  are  necessary  to  make  our  position 
clear  on  the  second  point  raised  by  Mill,  namely,  the 
importance  usually  given  to  one  of  the  conditions 
of  an  event  and  naming  this  the  cause.  Prac- 
tically, as  Mill  pointed  out,  the  fact  selected  is 
usually  the  one  which  is  nearest  in  time  to  the  effect. 
But,  as  we  have  seen,  the  immediate  temporal  ante- 
cedence of  the  cause  is  not  necessarily  an  essential 
feature  of  the  causal  relation.  What  rather,  even  for 
the  practical  view,  is  needed  is  the  selection  of  an 
agent  on  which  reliance  can  be  placed  to  bring  about 


CAUSATION  455 

the  desired  result.  Certainty  as  to  the  cause  seems 
to  be  the  desideratum,  whether  the  causal  factor  is 
the  immediate  temporal  antecedent  of  the  effect  or 
not.  When,  for  example,  we  wish  to  rid  the  prem- 
ises of  rats,  to  borrow  an  illustration,  we  may 
choose  either  traps,  strychnine,  phosphorus,  or  ter- 
riers, and  doubtless  the  one  selected  will  be  the  one 
that,  under  the  circumstances,  is  regarded  as  most 
efficient.  And  by  efficient,  in  this  connection,  we 
mean  the  one  that,  with  due  regard  to  the  circum- 
stances of  the  case,  realises  best  the  purpose  for 
which  it  is  chosen.  Now  when  the  purposes,  for 
the  satisfaction  of  which  causal  relations  are  sought, 
become  specialised  as  they  do  in  science,  when, 
that  is,  they  are  directed  toward  the  attainment  of 
knowledge,  and  not  toward  the  improvement  of  the 
material  conditions  of  life,  the  situation,  so  far  as 
the  causal  relation  is  concerned,  is  not  greatly  dif- 
ferent, for  in  science  the  search  for  a  cause  is 
determined  by  a  purpose  which  the  ascertainment 
of  the  cause  itself  is  expected  to  satisfy.  In  the 
field  of  science,  as  was  pointed  out  before,  the  pur- 
pose that  directs  an  inquiry  does  not  lie  outside  of, 
but  is  one  with,  the  attainment  of  scientific  truth. 
In  this  the  chief  difference  between  the  theoretical 
and  practical  life  is  to  be  found.  But  when  we  have 
said  that,  it  remains  true  that  the  conditions  of 
knowledge  are  more  rigid  than  those  of  practice, 
and  the  goal  of  inquiry  requires  more  strict  defini- 
tion. Hence  we  find  that  what  passes  for  a  cause  in 
practical  life  may  seem,  from  the  scientific  point  of 


456  A  TEXT-BOOK  OF  LOGIC 

view,  altogether  inadequate,  if  not  false,  and,  con- 
sequently, that  a  more  thorough  analysis  of  the 
antecedent  and  concurrent  circumstances  has  to  be 
undertaken  if  the  end  of  scientific  truth  is  to  be 
reached.  Now,  whether  or  not,  for  the  purpose  of 
science,  all  or  only  part  of  the  circumstances  and 
conditions  of  an  event  are  included  in  its  cause  will 
depend  on  the  particular  and  immediate  purpose  it 
is  intended  to  satisfy.  No  doubt,  the  ultimate  goal 
of  science  is  to  discover  laws  of  connection  which 
are  capable  of  extension  to  other  than  the  observed 
phenomena,  but,  at  the  same  time,  we  should  observe 
that  it  can  reach  this  end  only  by  the  determination 
of  the  particular  connections  of  one  empirical  event 
with  another  in  human  experience.  But  even  in 
this  more  restricted  field  of  scientific  effort,  a  cer- 
tain rigid  demand  is  usually  made  and  observed, 
namely,  that  all  and  only  those  factors  which  can 
be  regarded  as  essential  conditions  of  a  fact  or 
event  should  be  enumerated  as  its  cause.  It  is  only 
when  there  is  a  lapse  from  strict  scientific  precision 
that  any  thing  less  is  possible ;  and  even  when  such 
lapse  takes  place,  the  scientist  feels  himself  obliged 
to  fill  out,  on  demand,  the  scantier  statement  by 
restoring  all  the  enumerated  elements  that  are  of 
material  importance  to  our  understanding  of  the 
case. 

The  Necessity  of  Causal  Events.  The  two  fac- 
tors of  Mill's  view  of  Causation  that  we  have  con- 
sidered are,  first,  that  causes  are  invariable  ante- 
cedents of  the  facts  or  events  we  call  effects,  an»i 


CAUSATION  457 

second,  that  causes  are  always  complex  groups  of 
fact,  the  sum  total  of  conditions,  as  Mill  says, 
requisite  to  bring  the  effect  into  existence.  There 
is  still  a  third  factor  to  which  we  may  now  give 
attention,  a  factor,  it  would  seem,  that  occupies,  in 
Mill's  total  view,  a  place  which  gives  it  a  peculiarly 
special  prominence.  For,  according  to  Mill,  you 
may  have  a  sequence  displaying  the  features  of  com- 
plexity and  invariability  and  not  have  one  that  is 
definitely  causal.  That  is  to  say,  B  may  have  fol- 
lowed A  invariably  in  our  experience,  and  yet  the 
ground  or  cause  of  the  sequence  A-B  may  really 
not  be  in  A  at  all.  The  illustration,  borrowed  from 
Reid,  that  Mill  uses  is  the  sequence  of  night  and 
day,  in  neither  of  which  can  the  cause  of  the  other 
be  found,  although  there  is  no  doubt  that  the  em- 
pirical connection  extends  throughout  human  expe- 
rience. Some  other  factor,  therefore,  is  required 
to  complete  the  idea  of  cause,  for,  as  Mill  says,  "it 
is  necessary  to  our  using  the  word  cause  that  we 
should  believe  not  only  that  the  antecedent  always 
has  been  followed  by  the  consequent,  but  that  as 
long  as  the  present  constitution  of  things  endures 
it  always  will  be  so."  Unless  the  sequence  can  also 
be  regarded  as  'unconditional,'  we  are  not  war- 
ranted, by  Mill's  view,  in  considering  it  to  be  caus- 
ally determined.  "This  is  what  writers  mean  when 
they  say  that  the  notion  of  cause  involves  the  idea 
of  necessity.  .  .  .  That  which  is  necessary,  that 
which  must  be,  means  that  which  will  be,  whatever 
supposition  we  may  make  in  regard  to  all  other 


458  A  TEXT-BOOK  OF  LOGIC 

things.  .  .  .  That  which  will  be  followed  by  a 
given  consequence  when,  and  only  when,  some  third 
circumstance  also  exists,  is  not  the  cause,  even 
though  no  case  should  ever  have  occurred  in  which 
the  phenomenon  took  place  without  it.  Invariable 
sequence,  therefore,  is  not  synonymous  with  caus- 
ation, unless  the  sequence  besides  being  invariable, 
is  unconditional." 

It  will  be  seen,  at  once,  that  in  this  statement, 
and  only  here,  do  we  come,  in  Mill's  view,  face  to 
face  with  the  question,  crucial  for  our  comprehen- 
sion of  causal  relations,  of  what  we  must  mean 
when  we  say  that  one  event  is  necessarily  connected 
with  another.  Now  it  should  be  remarked  that  this 
statement  of  Mill's  raises  questions  which  for  their 
adequate  discussion  would  require  us  to  go  outside 
the  limits  of  inductive  logic  into  the  field  of  general 
metaphysics ;  and  this  is  true,  not  only  for  a  student 
of  the  theory  Mill  proposes,  but  it  is  admitted  as 
necessarily  so  by  Mill  himself.  For,  as  he  says,  it  is 
only  so  long  as  we  can  believe  that  the  "present 
constitution  of  things  endures,"  only  so  long,  that 
is,  as  "the  ultimate  laws  of  nature  (whatever  they 
may  be)  as  distinguished  from  the  derivative  laws 
and  the  collocations"  remain  unchanged,  that  what 
happens  in  experience  can  become  a  clue  to  what 
is  true  outside  experience.  In  other  words,  it  is 
only  so  long  as  the  nature  of  reality  is  and  remains 
what  it  is  that  we  can  argue  from  what  has  been 
to  what  will  be  in  human  experience.  But  the 
determination  of  the  nature  of  reality,  and  of  the 


CAUSATION  459 

relation  that  we  as  thinking  and  active  individuals 
sustain  toward  it,  is  the  definite  problem  of  meta- 
physics, and  only  indirectly  does  this  problem  come 
into  view  in  the  discussion  of  logical  questions.  But 
even  incidentally  it  is  worth  while  to  remark  that 
the  relation  of  logic  to  metaphysics  that  the  position 
of  Mill  raises  is  such  that,  unless  we  can  presuppose 
an  ordered  system  of  reality  of  some  sort,  our  con- 
fidence in  human  knowledge  is  ultimately  shaken, 
and  the  distinction  between  truth  and  error  to  a 
large  extent  is  obliterated.  For,  as  we  have  seen 
throughout,  the  nerve  of  human  knowledge  is  to  be 
found  in  the  confidence  we  have  that  in  all  science 
and  philosophy,  and,  we  should  say,  in  all  art  and 
religion  as  well,  we  are  interpreting,  not  the  empty 
shadows  of  a  merely  temporal  experience,  but  the 
real  nature  of  the  world  which  is  not  only  the  sub- 
stance of  all  our  knowing,  but  the  very  centre  and 
core  of  the  being  which  we  as  individuals  possess. 

Turning,  now,  from  these  rather  abstruce  con- 
siderations, we  must  try  to  interpret  Mill's  position 
with  respect  to  its  logical  implications.  In  order 
that  we  may  understand  exactly  what  Mill  had  in 
mind  to  say,  it  will  be  necessary  to  gain  and  secure 
a  correct  notion  of  the  term  in  which  he  translates 
the  necessity  that  belongs,  as  he  and  Hume  before 
him  admit,  to  our  notion  of  cause.  According  to  Mill, 
the  necessity  that  we  ascribe  to  a  causal  sequence 
has  its  foundation  in  the  unconditional  character 
of  the  causal  sequence.  What,  then,  does  Mill  mean 
by  unconditional?  The  meaning  that  Mill  attaches, 


460  A  TEXT-BOOK  OF  LOGIC 

in  a  general  way,  to  this  word  is  perhaps  not  diffi- 
cult to  detect,  although  he  does  not  state  definitely 
the  sense  in  which  it  is  understood.  Most  of  his 
statements  about  it  are  negative.  He  says,  for  in- 
stance, that  "that  which  will  be  followed  by  a  given 
consequent  when,  and  only  when,  some  third  cir- 
cumstance exists,  is  not  the  cause,"  the  meaning 
evidently  being  that  it  is  a  cause  only  when  the 
consequent  follows  without  such  mediation.  And, 
again,  he  says  that  "if  we  adopt  the  convenient 
modification  of  the  meaning  of  the  word  cause  which 
confines  it  to  the  assemblage  of  positive  conditions 
without  the  negative,  then  instead  of  "uncondition- 
ally," we  must  say,  "subject  to  no  other  than  neg- 
ative conditions,"  where,  again,  the  absence  of  some 
third  circumstance  is  necessary  for  determining  an 
unconditional  sequence.  The  point  that  Mill  seems 
to  make  is  that  a  sequence  is  unconditional  when  the 
consequent  is  seen  to  follow  from  the  totality  of 
conditions  which  constitute  its  cause,  without  any 
aid  from  any  other  circumstance  which  falls  outside 
its  cause  as  thus  determined. 

Two  remarks  may  help  to  make  the  meaning  of 
this  statement  clearer.  In  the  first  place,  Mill's 
view  leaves  out  of  account,  as  indeed  it  has  a  right 
to,  such  metaphysical  considerations  as  were  re- 
ferred to  a  little  while  ago.  However  impossible 
such  a  procedure  would  be  if  Mill  were  discussing 
the  causal  problem  from  the  standpoint  of  the  phil- 
osophy of  knowledge,  it  is  quite  possible  and  even 
necessary  when  he  is  concerned  merely  with  the 


CAUSATION  461 

invariable  connections  that  are  built  up  in  the  course 
of  human  experience.  The  denial,  therefore,  that 
any  "third  circumstance"  operates  in  an  uncondi- 
tional sequence  cannot  be  meant,  by  Mill,  to  refer 
to  the  "constitution  of  things"  which,  as  we  saw, 
is  in  some  sort  the  foundation  on  which  all  human 
knowledge  in  the  long  run  depends.  In  the  second 
place,  we  may  remark  that  the  "third  circumstance," 
on  the  absence  of  which  from  any  sequence  the 
unconditionality  of  the  cause  is  determined,  must  be 
interpreted  to  mean  some  third  phenomenal  circum- 
stance, some  further  fact  or  event  of  human  expe- 
rience the  same  in  kind  as  those  that  enter  into  the 
causal  relation.  What  this  statement  amounts  to 
is  the  declaration  that  whenever  any  causal  se- 
quence has  been  determined,  it  will  be  found  to 
include  all  those  positive  factors  on  which  the  occur- 
rence of  the  phenomenon  depends,  and  that  it  is 
only  when  all  such  factors  are  present  that  the 
sequence  is  necessary,  or,  in  Mill's  term,  uncondi- 
tional. It  may  help  to  bring  out  the  significance  of 
such  a  statement  if  we  say  that  when  the  stated 
conditions  are  satisfied  in  any  given  case,  we  can 
argue  not  only  from  the  occurrence  of  the  cause  to 
the  occurrence  of  the  effect,  but  also  from  the  occur- 
rence of  the  effect  to  the  occurrence  of  the  cause. 
The  presence  of  either  the  cause  or  effect  necssarily 
implies  the  presence  also  of  the  effect  or  the  cause. 
The  Plurality  of  Causes.  In  view  of  the  fact  that 
the  aim  of  science  is  to  point  out  a  connection  be- 
tween a  particular  event  and  the  totality  of  condi- 


462  A  TEXT-BOOK  OF  LOGIC 

tions  on  the  presence  of  which  the  event  takes  place, 
and  on  the  absence  of  which  it  does  not  take  place, 
we  may  ask  how  this  conception  of  the  aim  of 
science  is  affected  by  the  fact  that  the  same  event 
may  occur  for  very  different  reasons.  Now  about 
such  a  fact  there  is  no  qusetion.  It  was  fully  recog- 
nised, for  instance,  by  Mill  who  tersely  remarks 
that  "it  is  not  true  that  the  same  phenomenon  is 
always  produced  by  the  same  cause."  The  fact, 
then,  is  that  an  event  M  may  be  caused  now  by  A, 
and,  again,  by  B  or  C  or  D.  This  fact  is  known,  in 
the  terminology  of  Mill,  as  the  plurality  of  causes. 
What  effect,  we  may  ask,  does  the  recognition  of 
such  a  plurality  of  causes  have  upon  our  view  of 
the  nature  of  causation  as  expounded  in  the  pre- 
ceding paragraphs? 

If  we  consider  this  question  strictly  from  the 
point  of  view  of  what  we  have  seen  the  relations 
between  cause  and  effect  in  a  causal  sequence  must 
be,  it  is  obvious  that  we  can  not  regard  those  events 
whose  occurrence  depends  on  a  possible  plurality  of 
antecedents  as  causally  related  events  at  all.  It 
was  said  just  now  that  in  a  causal  sequence  we  must 
be  able,  not  only  to  argue  from  the  occurrence  of 
the  antecedent  to  that  of  the  consequent,  but  also 
to  argue  from  the  occurrence  of  the  consequent  to 
that  of  the  antecedent.  Now  the  significance  of 
such  a  connection  between  antecedent  and  conse- 
quent in  a  causal  sequence  is  that  it  goes  far  beyond 
what,  in  an  earlier  chapter,  we  saw  was  formally 
possible  when  we  were  considering  merely  hypo- 


CAUSATION  463 

thetical  statements  of  fact.  The  rule  concerning 
hypothetical  statements,  'If  A  then  B'  for  example, 
made  it  clear  that  from  the  occurrence  of  B  we 
could  say  nothing  with  respect  to  the  occurrence 
of  A,  and  the  reason  assigned  was  that  B  might 
have  occurred  for  some  other  reason  than  A.  In 
other  words,  we  had  to  recognise  the  possibility  of 
what  Mill  calls  the  plurality  of  causes.  Now  the 
necessity  for  such  a  rule  for  dealing  with  the  facts 
of  our  general  experience  is  quite  obvious  when  we 
consider  that,  with  the  development  of  science,  there 
has  come  to  be  recognised  a  marked  difference  be- 
tween empirically  connected  events  and  causally 
related  events,  and,  consequently  that  until  the 
causal  character  of  a  particular  sequence  has  been 
established,  we  cannot  be  certain  that  one  rather 
than  another  group  of  possible  antecedent  condi- 
tions, as  a  matter  of  fact,  has  been  the  occasion  of 
any  given  consequent. 

We  may  also  point  out  that  the  recognition  of  a 
plurality  of  causes,  if  we  emphasise  the  word  cause 
in  Mill's  phrase,  would  necessarily  throw  our  whole 
conception  of  cause  into  confusion,  and  there  would 
remain  for  us  no  means  of  distinguishing  between 
those  events  which  were  really  connected  'as  cause 
and  effect,  and  those  whose  connections  depended, 
in  MilPs  words,  on  some  "third  circumstance," 
events,  that  is  to  say,  which  are  connected  merely 
after  the  manner  of  an  empirical  juxtaposition. 
The  distinction  between  causal  sequences  and  em- 
pirical ones  is  important,  it  marks  one  of  the  gains 


464  A  TEXT-BOOK  OF  LOGIC 

that  have  been  acquired  as  the  result  of  much 
labour,  and  it  serves  the  distinctive  purpose  of  map- 
ping out  the  fields  with  respect  to  which  we  may 
claim  to  have  different  degrees  of  knowledge.  It 
is  certainly  true,  for  instance,  that  the  inferences 
drawn  from  our  ordinary  experience  are  enter- 
tained much  less  confidently  than  are  those  that 
rest  on  the  foundation  of  a  scientific  induction.  In 
the  latter  case  alone  do  we  have  certainty;  in  the 
former,  we  reach  only  a  higher  or  lower  degree  of 
probability.  And  the  difference  between  certainty 
and  probability  rests,  in  part  at  least,  on  the  fact 
that  in  the  case  of  certain  knowledge  all  the  factors 
material  to  it  are  known,  and  in  the  case  of  prob- 
ability we  have  no  reason  for  believing  that  this 
requirement  has  been  satisfied.  And  this  statement 
enables  us  to  see  why  it  is  that  analysis  plays  so 
large  a  part  in  the  method  not  only  of  the  sciences 
but  of  philosophy  as  well,  and  why  it  is  that,  from 
the  times  of  the  Greeks,  the  distinction,  based  on  the 
application  of  a  method  of  analysis  to  the  facts  of 
experience,  between  opinion  and  knowledge,  be- 
tween the  popular  beliefs  of  an  age  on  the  one  hand, 
and  carefully  established  truths  on  the  other,  has 
been  regarded  as  a  condition  of  intellectual  culture 
and  progress.  We  cannot,  therefore,  entertain  any 
suggestion  of  treating  the  two  classes  of  connection, 
the  causal  and  the  empirical,  as  if  no  distinction  had 
been  made  between  them,  and  we  cannot  do  so  be- 
cause all  scientific  advancement  depends  on  it,  and 


CAUSATION  465 

because  it  would  leave  us  without  any  adequate 
conception  of  what  we  should  mean  by  a  cause. 

The  result  of  our  consideration  of  the  conception 
of  a  plurality  of  causes  amounts  to  this,  that  when 
we  look  at  the  conception  from  the  standpoint  of  a 
carefully  stated  view  of  what  causation  implies,  it 
seems  to  be  a  quite  misleading,  if  not  mischievous, 
conception.  But,  it  may  be  objected,  this  result  can 
be  reached  and  maintained  only  if  we  allow  a  some- 
what strict  interpretation  of  the  causal  relation  to 
determine  the  view  we  take  as  to  the  possibility  of  a 
plurality  of  causes.  That  is  exactly  true.  But  the 
recognition  of  its  truth  does  not  require  us  to  alter 
our  notion  of  the  causal  relation,  but  to  indicate  the 
field  within  which  the  operation  of  more  than  a 
single  set  of  antecedents  as  a  condition  of  the  occur- 
,rence  of  a  given  fact  or  event  may  be  said  to  occur. 
What  we  have  seen  is  that  the  field  of  causally  estab- 
lished relations  is  not  such  a  field.  For  science  in  the 
strict  sense  of  that  term  there  is  only  one  group  of 
conditions  that  can  be  inferred  from  the  occurrence 
of  any  given  event.  But  when  we  remark  that,  as 
compared  with  the  broad  extent  of  our  ordinary 
experience,  the  causal  field  is  only  a  very  small 
area,  we  see  at  once  that,  when  we  go  outside  this 
field,  there  must  be  possible  some  other  than  a 
causal  interpretation  of  the  sequences  that  occur. 
It  follows,  therefore,  that  we  must  go  outside  the 
field  of  the  natural  sciences  if,  looking  at  our  expe- 
riences from  the  standpoint  of  their  temporal  rela- 


466  A  TEXT-BOOK  OF  LOGIC 

tions,  we  wish  to  emphasise  and  illustrate  the  possi- 
bility and  nature  of  a  plurality  of  causes.  Nowhere, 
except  in  the  sciences,  can  we  argue  from  conse- 
quent to  antecedent.  The  relations  of  antecedent 
and  consequent,  therefore,  that  occur  in  our  ordi- 
nary experience,  are  not,  in  the  strict  sense,  causal 
relations  at  all.  And  because  they  are  not,  it  seems 
altogether  misleading  to  speak  of  these  relations  as 
involving  a  plurality  of  causes.  What  a  discussion 
of  the  possibility  of  a  plurality  of  causes  forces  on 
us  is,  then,  the  recognition  of  a  type  of  experience 
which  implies  no  more  than  a  plurality  of  ante- 
cedent or  concurrent  conditions.  To  call  these  con- 
ditions, in  their  relation  to  the  event  with  which 
they  are  connected  in  our  experience,  causal  is  to 
go  beyond  what  we  know  about  them;  for,  as  we 
have  said,  the  test  of  a  causal  relation  is  that  we 
can  argue,  not  only  from  a  given  set  of  conditions 
to  the  conditioned,  but  also  from  the  conditioned 
to  a  particular  set  of  conditions.  It  is  exactly  the 
impossibility  of  doing  this  latter  that  led  Mill,  in 
the  class  of  cases  we  are  now  considering,  to  speak 
of  a  pluarlity  of  causes,  and  which  leads  us  to  speak 
of  a  plurality  of  conditions.  If,  by  our  terminology, 
we  can  keep  clearly  before  ourselves  the  fact  that 
the  relations  which  we  are  now  considering  are  not 
causal,  in  the  strict  sense  of  that  word,  but  that  they 
are  connected  empirically  merely  in  our  experience, 
it  will  be  passible  to  set  over  against  each  other  the 
two  types  of  experience,  and  to  entertain  the  prob- 
lem, which  the  non-causal  relations  certainly  sug- 


CAUSATION  467 

gest,  whether  these  latter  can  all  be  reduced  to  a 
single  causal  type.  Although  it  takes  us  outside  the 
limits  of  our  present  inquiry,  we  may  hazard  the 
remark  that  perhaps  human  life  and  experience  are 
too  rich  and  complex  to  be  capable  of  interpretation 
throughout  in  terms  of  any  single  class  of  relations. 

REFERENCES 

H.  A.  Aikins,  The  Problem  of  Logic,  Chs.  XXVI.,  XXVII., 
XXVIII.,  XXIX. 

J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Chs. 
XVI.,  XVII. 

J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Chs.  IV.,  V., 
VI.,  VII.,  VIII.,  IX.,  X. 

W.  S.  Jevons,  Elementary  Lessons  in  Logic,  Lessons  XXVIII., 
XXIX. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  IX. 

W.  Minto,  Logic,  Inductive  and  Deductive,  Chs.  III.,  IV.,  V., 
VI.,  VII. 

C.  Read,  Logic,  Deductive  and  Inductive,  3d  Edition,  Chs. 
XIV.,  XVI. 

W.  J.  Taylor,  Elementary  Logic,  Ch.  XVII. 

ADVANCED 

B.  Bosanquet,  Logic,  Vol.  I.,  Book  I.,  Ch.  VII. 

F.  H.  Bradley,  The  Principles  of  Logic,  Book.  II.,  Part  II., 

Ch.  III.,  Book  III.,  Part  II.,  Ch.  II. 
W.  R.  B.  Gibson,  The  Problem  of  Logic,  Chs.  XLII.,  XLIV., 

XLV.,  XLVI. 
H.  W.  B.  Joseph,  An  Introduction  of  Logic,  Chs.  XIX.,  XX., 

XXII. 
J.  S.  Mill,  A  System  of  Logic,  Book  III.,  Chs.  V.,  VI.,  VIII., 

IX.,  X.,  V. 


468  A  TEXT-BOOK  OF  LOGIC 

F.  C.  S.  Schiller,  Formal  Logic,  Chs.  XX.,  XXI. 
J.  Venn,  Empirical  Logic,  Ch.  XVII. 

J.  Welton,  A  Manual  of  Logic,  Vol.  II.,  Book  V.,  Chs.  I., 
§§  143,  144,  V.,  §  155. 

QUESTIONS 

1.  In  what  general  fact  of  observation  does  the  problem  of 
causation  originate? 

2.  How,  in  view  of  this  fact,  may  the  causal  problem  be 
stated? 

3.  Explain  what  is  meant  by  saying  that  the  causal  prob- 
lem is  practical  before  it  is  theoretical.    Illustrate. 

4.  In  what  way  does  the  practical  aspect  of  the  problem  of 
causation  tend  to  develop  human  intelligence? 

5.  Describe  as  accurately  as  you  can  the  precise  nature  of 
the  regularities  in  experience  which  we  are  led  to  ob- 
serve from  the  practical  point  of  view. 

6.  In  what  two  respects  does  the  theoretical  differ  from  the 
practical  view  of  causation,  and  what  advantages  are 
thereby  secured? 

7.  State  and  illustrate  Mill's  criticism  of  the  practical  and 
theoretical  conceptions  of  cause. 

8.  Show,  by  means  of  illustrations,  that  the  practical  and 
theoretical  conceptions  of  cause  are  genetically  related. 

9.  In  what  way  has  the  theoretical  notion  of  cause  reacted 
upon  the  practical  to  give  it  a  more  definite  and  extended 
meaning? 

10.  What  is  meant  by  saying  that  the  causal  problem  arises 
from  the  importance  of  order  in  human  experience? 

11.  'The  causal  problem  is  concerned  with  the  question  of 
how  things  happen  as  they  do.'    Explain. 

12.  What,  according  to  Mill,  is  the  first  characteristic  of  a 
causal  relation? 

13.  What  is  meant  by  the  time  relations  of  causal  events? 

14.  How  far  do  you  agree  with  Mill  that  the  cause  of  an 
event  is  its  invariable  antecedent? 


CAUSATION  469 

15.  What  can  you  say  with  respect  to  the  view  that  there 
is  no  essential  difference  between  a  cause  and  an  effect. 

16.  Explain  what  is  meant  by  the  temporal  continuity  of 
causal  events. 

17.  What,  according  to  Mill,  is  the  second  characteristic  of 
causal  relations,  and  to  what  two  facts  of  importance 
does  it  direct  attention? 

18.  What  does  Jevons  mean  by  the  occasion  of  an  event  as 
contrasted  with  its  cause?     What  other  term  is  some- 
times used  for  Jevons'  'occasion'? 

19.  Give  three  reasons  for  emphasising  the  complex  charac- 
ter of  causes. 

20.  What  can  be  said  for  and  against  selecting  one  of  the 
conditions  of  an  event  and  calling  that  the  cause? 

21.  In  what  way  would  your  answer  to  the  previous  ques- 
tion be  affected  by  the  consideration  that  one's  interest 
in  the  causal  relation  is  practical  and  not  theoretical? 

22.  What,  according  to  Mill,  is  the  third  characteristic  of 
causal  relations? 

23.  Does  Mill  recognise  the  'necessity'  of  causal  relations, 
and,  if  so,  what  does  he  mean  by  necessity? 

24.  Does  Mill's  view  of  causation  imply  an  appeal  to  meta- 
physics, and,  if  so,  in  what  respect? 

25.  Explain  what  Mill  means  by  unconditional. 

26.  Is  it  possible,  on  Mill's  view  of  causation,  to  argue  from 
the  occurrence  of  an  effect  to  that  of  the  cause? 

27.  What  is  meant  by  the  plurality  of  causes? 

28.  If  in  any  particular  instance  we  admit  a  possible  plu- 
rality of  causes,  how  does  that  admission  affect  our  con- 
ception of  its  strictly  causal  character? 

29.  What  is  the  difference  between  causally  and  hypothet- 
ically  connected  series  of  events? 

80.     Why  would  it  be  preferable  to  speak  of  a  plurality  of 
eonditions  instead  of  a  plurality  of  causes? 


470  A  TEXT-BOOK  OF  LOGIC 


EXERCISES 

1.  Enumerate  six  instances  of  regularity  in  the  order  of 
particular  events  which  are  of  importance  for  the  prac- 
tical life. 

2.  Develop,   from   the  theoretical   point   of  view,   the  in- 
stances mentioned  in  your  answer  to  the  previous  ques- 
tion in  order  to  show  to  what  question  of  scientific  in- 
terest each  may  lead. 

3.  Examine  six  instances  of  scientific   causation  for  the 
purpose  of  showing  how  each  satisfies  the  three  condi- 
tions of  a  cause  mentioned  in  the  text. 

4.  Examine  the  following  and  show  in  what  respects  they 
are,  and  in  what  respects  they  are  not,  statements  of 
strictly  causal  relations. 

(1)  In  myexperience  A  has  been  invariably  preceded 
by  B,  and  we  may  therefore  conclude  that  B  is 
the  cause  of  A. 

(2)  Scarlet  poppies,  scarlet  verbenas,  the  scarlet  haw- 
thorne  and  honeysuckle  are  all  odourless,  there- 
fore we  may  conclude  that  all  scarlet  flowers  are 
destitute  of  odour. 

6.  Mention  six  instances  which  illustrate,  what  Mill  calls, 
a  plurality  of  causes.  State  for  each  instance  the  pos- 
sible causes. 


CHAPTER  XVII 

MILL'S  EXPERIMENTAL  METHODS 

Their  Historical  Position.  The  publication  of 
Mill's  System  of  Logic  in  1843  gave,  no  doubt,  a 
great  impetus  to  the  study  of  what  is  commonly 
known  as  inductive  logic,  and  especially  to  the  con- 
sideration of  the  principles  that  underlie  the  meth- 
ods by  which,  in  the  several  sciences,  causal  relations 
are  determined.  Prior  to  Mill,  however,  interest  in 
the  inductive  inquiry  had  had  a  somewhat  long  his- 
tory, and  the  reader  will  find  in  Minto's  Logic  (pp. 
243-272)  an  account  of  the  course  that  this  interest 
took  from  the  time  of  the  Franciscan  monk,  Roger 
Bacon  (1214-1292),  to  the  modern  era  which  was 
ushered  in,  and  whose  development  was  determined 
by  the  progress  of  experimental  science.  That  the 
advancement  of  learning,  of  which  Francis  Bacon 
(1561-1626)  may  be  taken  as  the  modern  herald, 
should  have  maintained  itself  successfully  for  over 
two  centuries,  and  that  during  that  period  natural 
science  should  have  extended  its  scope  as  well  as 
secured  its  position,  could  not  be  without  its  in- 
fluence upon  the  conception  that  was  held  of  the 
nature  and  value  of  logical  inquiries.  In  the  pres- 
ence of  such  a  solid  body  of  achievement  as  came 
rapidly  to  the  credit  of  the  natural  sciences,  it  was 
inevitable  that  interest  should  be  aroused  in  the 
methods  by  which  such  results  were  gained.  Con- 

(471) 


472  A  TEXT-BOOK  OF  LOGIC 

sequently,  we  find  that  men  of  learning  in  this 
period  gave  considerable  attention  to  the  study  of 
scientific  methods,  and  in  the  first  half  of  the  nine- 
teenth century  HerscheFs  discourse  On  the  Study 
of  Natural  Philosophy,  (1831),  and  Whewell's  two 
large  volumes  on  the  History  of  the  Inductive  Sci- 
ences, (1837),  and  his  Philosophy  of  the  Inductive 
Sciences,  (1840),  stand  out  prominently  as  contri- 
butions of  capital  importance  to  our  understanding 
of  the  inductive  procedure.  Based  as  they  are  upon 
the  facts  of  experimental  science,  and  containing  a 
description  and  analysis  of  the  methods  by  which 
conclusions  had  been  reached  in  the  sciences,  they 
constitute  a  repository  of  great  value  for  any  one 
who  would  study  the  theory  of  inductive  science. 
With  these  books  before  him,  Mill  set  out  in  his 
Logic,  as  he  says,  to  "generalise  the  modes  of  inves- 
tigating truth  and  estimating  evidence,  by  which  so 
many  important  and  recondite  laws  of  nature  have, 
in  the  various  sciences,  been  aggregated  to  the 
stock  of  human  knowledge."  In  the  chapter  on  The 
Four  Methods  of  Experimental  Inquiry/  Mill  gives 
an  account  of  the  various  ways  in  which  causal 
relations  are  or  may  be  determined.  In  what  fol- 
lows, we  propose  to  describe  these  methods  briefly, 
and  shall  limit  ourselves  chiefly  to  the  task  of  stating 
and  illustrating  them.  To  determine  the  view  that 
Mill  took  of  them  as  a  whole,  or  to  estimate  their 
value  in  detail,  falls  outside  the  scope  of  an  elemen- 
tary study  of  logical  problems. 


MILL'S  EXPERIMENTAL  METHODS  473 

The  Nature  of  the  Problem  to  which  these  Methods 
Apply.  In  the  foregoing  chapter,  we  have  seen  that 
the  causal  relation,  strictly  interpreted,  is  reciprocal, 
that  is,  it  is  a  relation  between  phenomena  of  such 
a  kind  that  from  the  presence  or  absence  of  either 
term  of  the  relation  we  can  argue  to  the  presence 
or  absence  of  the  other.  The  rise  and  fall  of  the 
mercury  in  a  thermometer,  for  example,  are  recip- 
rocally related  to  the  varying  degrees  of  tempera- 
ture. To  the  establishment  of  such  relations  the 
sciences  doubtless  aspire  in  their  investigation  of 
the  processes  of  nature.  And  that  a  considerable 
degree  of  success  in  this  particular  has  been  achieved 
in  those  sciences,  such  as  physics  and  astronomy, 
which  rest  upon  a  mathematical  foundation  is  suffi- 
cient to  suggest,  to  those  who  are  interested  in  the 
logic  of  the  sciences,  an  inquiry  to  which  the  meth- 
ods of  Mill  are  the  direct  answer.  Mill's  methods,  in 
other  words,  are  a  statement  of  the  processes  which 
have  been  found  useful  in  the  establishment  of  those 
causal  relations  in  which  the  antecedent  and  conse- 
quent reciprocally  imply  each  other.  But  since  recip- 
rocal relations  have  not  been  established  between 
the  antecedent  and  the  consequent  of  all  known 
phenomena,  we  should  be  putting  an  unnecessary 
strain  upon  these  methods  if  we  did  not  regard  them 
as  applying,  in  the  strict  sense,  only  to  those  special 
cases  in  which  a  relation  of  the  kind  in  question 
had  been  determined.  We  may  also  remark  that 
these  methods  are  not  offered  by  Mill  as  a  substitute 
for  the  specialised  modes  of  investigation  which  are 


474  A  TEXT-BOOK  OF  LOGIC 

developed  by  each  special  science  according  to  its 
needs.  Indeed,  the  methods  are  quite  general  in 
nature,  and  could  not  have  been  formulated  had  not 
relations  of  the  kind  they  imply  been  already  suc- 
cessfully established.  They  must  be  understood, 
therefore,  as  revealing  the  logic  of  causal  inquiries, 
when  these  inquiries  have  led  to  the  determination 
of  reciprocal  relations  between  causes  and  effects. 

Elimination  as  a  Method  of  Causal  Inquiry.  We 
have  just  seen  that  Mill's  methods  aim  to  state  the 
general  modes  of  procedure  in  those  instances  in 
which  reciprocal  causal  relations  have  been  estab- 
lished. In  the  light  of  this  statement,  it  might  seem 
superfluous  to  ask  whether  the  causal  inquiry  rests 
upon  the  process  of  eliminating  from  the  cause,  or 
effect,  those  data  whose  presence  or  absence  from  a 
phenomenon  makes  no  difference  either  to  its  occur- 
rence or  non-occurrence.  This  is,  indeed,  the  posi- 
tion that  we  should  be  inclined  to  adopt  were  it  not 
for  the  fact  that  a  difference  of  opinion  exists  as  to 
whether,  and  in  what  sense,  the  methods,  as  Mill 
expounds  them,  depend  upon  such  process  of 
elimination. 

Joseph,  for  example,  takes  the  view  that  "the 
causal  circumstances  are  indicated  by  a  process  of 
exhaustive  elimination."  His  position,  more  fully 
stated,  is  that,  in  view  of  the  nature  of  causal  rela- 
tions, certain  particular  requirements  must  be  satis- 
fied by  any  instance  which  claims  to  involve  a  causal 
relation,  and  that  the  failure  to  satisfy  any  one  of 
these  requirements  disproves  that  relation  between 
two  given  phenomena.  These  requirements  he  enu- 


MILL'S  EXPERIMENTAL   METHODS  475 

merates  as  grounds  of  elimination,  and  are  as  fol- 
lows: 

1.  Nothing  is  the  cause  of  a  phenomenon  in  the 
absence  of  which  it  nevertheless  occurs. 

2.  Nothing  is  the  cause  of  a  phenomenon  in  the 
presence  of  which  it  nevertheless  fails  to  occur. 

3.  Nothing  is  the  cause  of  a  phenomenon  which 
varies  when  it  is  constant,  or  is  constant  when  it 
varies,  or  varies  in  no  proportionate  manner  with  it. 

4.  Nothing  is  the  cause  of  a  phenomenon  which 
is  known  to  be  the  cause  of  a  different  phenomenon. 

These  grounds  of  elimination  are  said  by  Joseph 
to  be  the  foundations  of  Mill's  inductive  methods. 
The  first  is  the  foundation  of  the  Method  of  Agree- 
ment ;  the  second,  of  the  Method  of  Difference ;  the 
first  and  second  combined,  of  the  Joint  Method  of 
Agreement  and  difference;  the  third,  of  the  Method 
of  Concomitant  Variations;  and  the  fourth,  of  the 
Method  of  Residues.  It  thus  comes  about,  according 
to  Joseph,  that  "Mill  has  not  formulated  four  (or 
five)  but  one  "Method  of  Experimental  Inquiry" 
...  of  which  the  essence  is  that  you  establish 
a  particular  hypothesis  about  the  cause  of  a  phe- 
nomenon by  showing  that,  consitently  with  the 
nature  of  the  relation  of  cause  and  effect,  the  facts 
do  not  permit  you  to  regard  it  as  the  effect  of  any- 
thing else  (and  mutatis  mutandis  if  you  are  inquir- 
ing into  the  effect  of  anything) ."  Thus  if  I  know 
that  S  must  be  caused  by  L  or  M  or  P  or  Q,  because 
these  are  the  instances  in  which  the  phenomenon 
occurs,  then  by  testing  each  instance  by  the  canons 


476  A  TEXT-BOOK  OF  LOGIC 

of  elimination  I  am  able  to  discover  the  one  rela- 
tion in  which  S  stands  that  is  reciprocally  causal. 

Against  this  position  Gibson  argues  that  there 
is  in  Joseph's  account  a  confusion  between  physical 
and  logical  elimination,  and  that  when  Mill  speaks 
of  the  Methods  of  Agreement  and  Difference  as 
methods  of  elimination  he  must  be  understood  to 
mean  the  former  and  not  the  latter  kind  of  elimina- 
tion. The  meaning  of  this  contention  is  quite  clear 
if  by  physical  elimination  is  understood  the  method 
of  excluding  from  a  phenomenon  certain  elements 
which  are  found  not  to  have  an  effect  upon  the  occur- 
rence or  non-occurrence  of  the  phenomenon.  By 
logical  elimination,  on  the  other  hand,  is  meant  the 
rejection  of  certain  hypotheses  —  as,  for  example, 
some  of  the  alternatives  in  a  disjunctive  proposi- 
tion—  with  respect  to  the  causal  connection.  In 
this  case,  we  are  rejecting  the  non-causes  as  a 
means  of  discovering  the  true  causes.  There  is  a 
certain  presumption  in  favour  of  Gibson's  conten- 
tion, for  Mill  himself  says  that  elimination  is  a  term 
"well  suited  to  express  the  operation  .  .  .  which 
has  been  understood  since  the  time  of  Bacon  to  be 
the  foundation  of  experimental  inquiry  —  namely, 
the  successive  exclusion  of  the  various  circumstances 
which  are  found  to  accompany  a  phenomenon  in  a 
given  instance,  in  order  to  ascertain  what  are  those 
among  them  which  can  be  absent  consistently  with 
the  existence  of  the  phenomenon."  But  whether 
any  or  all  of  Mill's  Methods  are  based  upon  a  single 
type  of  elimination  can  be  decided  only  by  exam- 


MILL'S  EXPERIMENTAL   METHODS  477 

ining  the  methods  themselves.  For  the  present,  it  is 
enough  to  have  stated  the  nature  of  the  difference 
between  the  views  that  are  held  of  the  relation  of 
elimination  to  the  Methods  that  we  are  about  to 
study. 

The  Method  of  Agreement.  Mill  states  the  prin- 
ciple upon  which  this  Method  rests  as  follows: 
If  two  or  more  instances  of  the  phenomenon  under 
investigation  have  only  one  circumstance  in  common, 
the  circumstance  in  which  alone  all  the  instances  agree 
is  the  cause  (or  effect)  of  the  given  phenomenon. 
The  requirement  that  the  instances  in  question 
shall  have  only  one  circumstance  in  common  can  not 
be  satisfied  unless  all  the  other  circumstances  that 
are  relevant  to  the  phenomenon  are  different.  Not 
any  enumeration  of  instances,  therefore,  would  sat- 
isfy the  conditions  of  this  Method,  but  only  one  in 
which  all  the  instances,  however  much  they  may 
differ  from  one  another,  are  alike  in  only  a  single 
particular.  When,  then,  two  or  more  instances  of  a 
phenomenon  are  shown  to  have  only  one  circum- 
stance in  common,  that  circumstance,  according  to 
Mill,  is  the  cause  or  the  effect  of  the  phenomenon.  For 
this  reason,  the  Method  has  been  called  the  Method 
of  Single  Agreement,  and  is  formulated  by  Jevons 
as  follows :  The  sole  invariable  antecedent  of  a  phe- 
nomenon is  probably  its  cause.  An  illustration  bor- 
rowed from  Bain,  may  be  given.  "The  North-East 
wind,"  Bain  writes,  "is  generally  detested  in  this 
country ;  as  long  as  it  blows,  few  people  are  at  their 
best.  Occasional  well  known  causes  of  a  wind  being 


478  A  TEXT-BOOK   OF  LOGIC 

injurious  are  violence,  excessive  heat  or  cold,  ex- 
cessive dryness  or  moisture,  electrical  condition,  the 
being  laden  with  dust  or  exhalations.  Let  the  hypo- 
thesis be  that  the  last  is  the  cause  of  the  North- 
East  wind's  unwholesome  quality;  since  we  know 
it  is  a  ground  current  setting  from  the  pole  toward 
the  equator  and  bent  westward  by  the  rotation  of 
the  earth;  so  that,  reaching  us  over  thousands  of 
miles  of  land,  it  may  well  be  fraught  with  dust, 
effluvia,  and  microbes.  Now,  examining  many 
cases  of  North-East  wind,  we  find  that  this  is  the 
only  circumstance  in  which  all  the  instances  agree; 
for  it  is  sometimes  cold,  sometimes  hot;  generally 
dry ;  but  sometimes  wet ;  sometimes  light,  sometimes 
violent;  and  of  all  electrical  conditions.  Each  of 
the  other  circumstances,  then,  can  be  omitted  with- 
out the  North-East  wind  ceasing  to  be  noxious ;  but 
one  circumstance  is  never  absent  —  namely,  that  it 
is  a  ground  current.  That  circumstance,  therefore, 
is  probably  the  cause  of  its  injuriousness." 

It  will  be  observed  from  this  illustration  that  the 
Method  is  essentially  a  method  of  elimination;  its 
use  depends  upon  the  possibility  of  analysing  the 
phenomenon  into  its  constituent  parts,  and  of  select- 
ing from  among  them  the  one  that  is  causal.  It  is 
evident,  therefore,  that  the  method  cannot  begin  to 
be  put  into  operation  until  we  have  before  us  at 
least  two  instances  of  the  phenomenon,  and  that 
the  reliability  of  the  Method  is  much  increased  with 
an  increase  in  the  number  and  variety  of  the  in- 
staces  that  are  examined.  In  view  of  such  facts 


MILL'S  EXPERIMENTAL   METHODS  479 

as  these,  Mellone  has  formulated  the  method  as 
follows:  When  observation  shows  that  two  events 
accompany  one  another  (either  simultaneously  or  in 
succession),  it  is  probable  that  they  are  causally  con- 
nected; and  the  probability  increases  with  the  number 
and  variety  of  the  instances. 

When  this  Method  speaks  of  causes  as  single 
antecedents,  it  is  evident  that  it  presupposes  that 
the  phenomenon  under  investigation  has  been  sub- 
jected to  analysis,  and  that  in  this  way  its  elements 
have  been  distinguished.  Now,  with  respect  to  the 
supposition  that  causes  are  to  be  discovered  among 
the  elements  into  which  the  phenomenon  is  anal- 
ysed, there  are  two  question  to  be  asked.  The  first 
is,  are  we  certain,  in  view  of  the  inter-connection 
of  all  parts  of  the  known  universe,  that  single  events 
ever  do  act  in  isolation  from  all  the  rest?  But  not 
to  press  the  point  in  that  form,  are  we  certain  that 
within  particular  universes,  that  is,  with  reference 
to  particular  groups  of  events,  we  can  analyse  a 
point  for  point  concomitance  between  causes  and 
effects?  For  instance,  is  the  "ground  current"  of 
the  illustration  used  above,  on  any  supposition,  a 
single  antecedent?  Is  it  not  merely  another  name 
for  "dust,  effluvia,  and  microbes"?  If,  however,  it 
be  replied  that  the  object  of  science  is  to  establish 
causal  connections  between  single  antecedents  and 
consequents,  we  may  ask,  in  the  second  place, 
whether  there  exists  any  means  of  assuring  our- 
selves that  the  analysis  of  a  particular  phenomenon, 
however  complete  it  may  seem,  has  succeeded  in 


480  A  TEXT-BOOK   OF  LOGIC 

detecting  all  of  the  factors  present  in  the  event  that 
we  call  its  cause?  For  a  long  time,  for  example, 
air  was  regarded  as  an  element;  and  even  since  its 
analysis  into  oxygen,  nitrogen,  hydrogen,  carbon 
dioxide,  etc.,  modern  chemistry  has  discovered  still 
other  elements  in  certain  quantities.  It  may  very 
well  happen,  therefore,  that  any  supposed  single 
antecedent  is  really  complex.  In  most  cases,  it  is 
only  a  relative  simplicity  that  can  be  attained,  a 
simplicity  that  is  met  with  at  the  point  where  our 
methods  of  analysis  are  unable  to  carry  us  any 
further.  We  conclude,  therefore,  that  the  Method 
states  an  ideal  that,  in  practice,  is  difficult  to  attain, 
and,  when  attained,  to  definitely  certify. 

What  degree  of  confidence,  we  may  ask,  may  be 
reposed  in  the  results  that  are  attained  by  the  use 
of  this  Method  ?  In  other  words,  what  are  the  limits 
of  its  usefulness?  To  be  more  specific  still,  is  it 
distinctively  a  method  by  which  we  are  able  to  ex- 
plain the  occurrence  of  phenomena?  This  question 
we  must  answer  in  the  negative.  The  Method  of 
Agreement  is,  as  one  has  said,  "a  mode  of  recon- 
noitering,"  a  method  for  delimiting  the  area. within 
which  causal  relations  may,  with  some  degree  of 
confidence,  be  expected  to  exist.  But  for  the  estab- 
lishment of  such  relations  we  should  have  to  pass 
beyond  the  method  itself.  Let  us  suppose,  for 
example,  that  three  instances  of  a  phenomenon  may 
be  analysed  in  the  following  schematic  way: 


MILL'S  EXPERIMENTAL  METHODS  481 

[ABC  x  /  z] 

Antecedents  1  A  E'  C  x/wj-  Consequents 


Are  we  certain,  in  such  a  case,  that  A,  the  circum- 
stance in  which  all  the  antecedents  agree,  is  the 
cause  of  the  phenomenon  ?  Starting  with  the  obser- 
vation of  x,  does  it  follow,  because  our  analysis  of 
all  the  instances  of  x  shows  A  to  be  the  one  element 
that  is  common  to  these  instances,  that  A  is,  there- 
fore, the  cause  of  x  ?  Mill  has  pointed  out  in  answer 
to  such  questions  that  their  affirmative  answer 
would  take  us  beyond  the  limits  of  this  Method, 
when  and  so  long  as  we  are  obliged  to  consider,  in 
our  interpretation  of  the  instances,  the  possibility 
of  a  plurality  of  causes,  the  possibility,  that  is,  that 
x  may  be  produced  by  more  than  one  cause.  If  the 
instances  of  the  phenomenon  were  known  to  be 
reciprocal,  or  if  we  were  certain  that  we  had  all 
the  instances  before  us,  the  situation  would  be 
different;  but  so  long  as  neither  condition  is  guar- 
anteed, it  only  remains  probable,  as  Jevons'  and 
Mellone's  formulations  of  the  Method  indicate,  that 
the  "one  circumstance  in  common"  is  the  cause  of 
the  phenomenon  in  question.  It  thus  appears,  to 
quote  Mill,  that  the  Method  of  Agreement  "leads 
only  ...  to  unifomities,  which  either  are  not  laws 
of  causation,  or  in  which  the  question  of  causation 
must  for  the  present  remain  undecided.  The  Method 
of  Agreement  is  chiefly  to  be  resorted  to  as  a  means 
of  suggesting  applications  of  the  Method  of  Differ- 

31 


482  A  TEXT-BOOK  OF  LOGIC 

ence,  ...  or  as  an  inferior  resource  in  case  the 
Method  of  Difference  is  impracticable;  which  .  .  . 
generally  arises  from  the  impossibility  of  artificially 
producing  the  phenomena/'  that  is,  when  experi- 
mentation is  not  possible. 

The  Method  of  Difference.  The  Method  of  Agree- 
ment, as  we  saw,  is  a  method  of  systematic  obser- 
vation, and  its  object,  negatively  stated,  is  to  elim- 
inate from  the  occurrences  of  a  particular  phenom- 
enon those  elements  which,  because  they  are  not 
constant  in  all  the  instances,  cannot  be  regarded  as 
being  the  cause,  or  part  of  the  cause  of  the  phenom- 
enon, and  thus,  affirmatively  stated,  to  map  out  the 
area  within  which  the  cause  may  probably  be  found. 
Turning  now  to  the  Method  of  Difference,  we  find 
that  it  is  a  method  of  scientific  experiment,  and 
the  formulation  given  it  by  Mill  is  as  follows:  If 
an  instance  in  which  the  phenomenon  under  inves- 
tigation occurs,  and  an  instance  in  which  it  does  not 
occur,  have  every  circumstance  in  common  save  one, 
that  one  occurring  only  in  the  former,  the  circum- 
stance in  which  alone  the  two  instances  differ  is  the 
effect,  or  the  cause,  or  an  indispensable  part  of  the 
cause,  of  the  phenomenon.  Let  us  suppose,  for  ex- 
ample, that  two  instances  of  a  phenomenon  can  be 
analysed  schematically  as  follows : 

f  A  B  C  x  y  zl 

Antecedents  }  I  Consequents 

B  C  y  z 


MILL'S  EXPERIMENTAL   METHODS  483 

then  we  may  say,  according  to  this  Method,  that  A 
is  the  cause  of  x.  Thus,  let  us  suppose  that  in  two 
glasses  equal  quantities  of  lemon  juice  and  water 
are  mixed,  and  that  in  one  of  them  a  given  quantity 
of  sugar  is  dissolved.  The  taste  of  the  liquid  which 
contains  the  sugar,  we  shall  say,  is  pleasant,  and 
the  taste  of  the  liquid  which  does  not  contain  sugar 
is  unpleasant.  What  is  the  cause  of  the  pleasant 
taste?  The  circumstance,  says  Mill,  in  which  alone 
the  two  instances  differ,  namely,  the  sugar. 

In  calling  the  Method  of  Difference  a  method  of 
scientific  experiment,  we  may  observe  that  scientific 
experimentation,  as  this  was  defined  above,  involves 
a  definite  control  of  the  conditions  under  which  a 
phenomenon  occurs,  and  a  definite  inquiry  to  which 
the  experiment  is  expected  to  give  an  affirmative  or 
negative  answer.  Scientific  experiment  is  like  a 
shafted  arrow,  it  is  aimed  at  a  mark,  and  its  course 
toward  that  mark  is  controlled,  as  is  the  arrow 
which  is  sped  from  the  bow.  To  illustrate,  let  us 
suppose  that  we  wished  to  know  why  a  feather, 
dropped  simultaneously  from  the  same  height  as  a 
coin,  reaches  the  ground  after  the  coin.  Our  ques- 
tion will  be,  Is  the  greater  resistance  offered  by  the 
air  to  the  feather  the  cause  of  the  observed  phe- 
nomenon? To  answer  this  question,  we  must  insti- 
tute an  experiment,  and  to  do  this,  as  we  said,  it  is 
necessary  to  bring  the  phenomenon  under  controlled 
conditions.  Thus,  we  first  drop  the  two  objects 
from  the  same  level  and  at  the  same  time  in,  let  us 
say,  the  receiver  of  an  air-pump.  The  feather  is 


484  A  TEXT-BOOK  OP  LOGIC 

observed  to  flutter  to  the  base  of  the  pump  after 
the  coin.  We  perform  the  same  experiment  again, 
with  the  exception  that  we  take  care  to  remove  all 
the  air  from  the  receiver.  Under  these  conditions, 
the  coin  and  the  feather  reach  the  base  of  the  re- 
ceiver at  the  same  time.  The  conclusion  is  that  the 
only  circumstance  in  which  the  two  instances  differ, 
namely,  the  presence  of  air  in  the  former,  is  the 
cause  of  the  phenomenon.  Because,  as  in  this  ex- 
ample, the  Method  proceeds  systematically  by 
changing  one  condition  at  a  time,  it  is  known  as 
the  Method  of  Single  Difference,  and  the  following 
formulation  has  been  given  by  Mellone:  When 
the  addition  of  an  agent  is  followed  by  the  ap- 
pearance, or  its  subtraction  by  the  disappearance,  of 
a  certain  event,  other  circumstances  remaining  the 
same,  that  agent  is  causally  connected  with  the  event. 
Or,  to  state  the  principle  on  which  any  formulation 
of  the  Method  relies,  we  may  say  that  the  circum- 
stance in  the  absence  of  which  a  phenomenon  fails  to 
occur  is  the  cause,  or  part  of  the  cause,  of  the  phe- 
nomenon. 

It  will  add  to  the  clearness  of  our  apprehension 
of  the  meaning  of  this  Method,  if  we  distinguish 
the  instances  of  the  phenomenon  that  are  success- 
ively observed.  For  this  purpose,  let  us  call  the 
instance  in  which  the  suspected  cause  occurs  the 
positive  instance,  and  the  one  in  which  it  does  not 
occur  the  negative  instance.  By  this  terminology 
is  meant  that,  in  what  is  called  the  positive  in- 
stance, we  have  the  occurrence  of  the  observed  phe- 


MILL'S   EXPERIMENTAL   METHODS  485 

nomenon  along  with  the  occurrence  of  its  supposed 
cause,  and,  in  the  negative  instance,  the  absence  of 
the  phenomenon  together  with  the  absence  of  the 
supposed  cause. 

In  view  of  this  distinction,  it  will  be  seen  that 
the  Method  depends,  for  its  validity,  on  the  negative 
instances  through  which  a  suspected  cause  is  either 
proved  or  disproved.  And,  for  this  reason,  it  rightly 
insists  on  the  importance  of  varying  only  one  condi- 
tion of  the  phenomenon  at  a  time.  For  if  we  were  to 
vary  simultaneously  two  of  a  phenomenon's  condi- 
tions, and  found  that  some  change  resulted,  we 
should  be  unable  to  tell  whether  this  change  was  due 
to  one  of  the  altered  conditions,  or  to  the  other,  or 
to  the  joint  action  of  both.  And  if  no  change  en- 
sued, we  could  not  safely  conclude  that  neither  con- 
dition was  affective,  for  the  action  of  the  one  may 
have  been  neutralised  by  that  of  the  other.  And 
even  when  only  a  single  condition  is  varied  at  any 
one  time,  it  is  important,  as  Mill  pointed  out,  that 
the  experiment  should  be  conducted  with  dispatch, 
and  its  entire  process  brought  as  rapidly  as  possible 
to  an  end.  The  reason  for  this  caution  is  that  if  the 
experiment  is  to  serve  the  purpose  for  which  it  was 
instituted,  the  effect  must  be  the  effect  solely  of  the 
one  altered  condition.  If,  on  the  contrary,  during 
the  course  of  an  unusually  prolonged  experiment, 
the  original  conditions  of  the  experiment  were  mod- 
ified by  the  development  of  changes  which  deter- 
mined in  part  the  character  of  the  observed  effect  we 
should  have,  what  Mill  called,  an  inter-mixture  of 


486  A  TEXT-BOOK   OF  LOGIC 

effects ;  and  this  would  be  as  destructive  of  the  value 
of  the  Method  as  any  unsystematic  variation  in  the 
conditions  themselves. 

It  is  a  well  known  fact  that  not  all  problems  are 
capable  of  experimental  handling,  and  that  those 
that  are,  are  liable  to  have  their  results  affected  by 
the  operation  of  conditions  which  we  can  in  no 
wise  eliminate.  In  the  former  case,  the  Method  of 
Difference  cannot  be  used.  In  the  latter,  the  condi- 
tions referred  to  are  those  that  belong  to  the  struc- 
ture of  the  universe  to  which  the  particular  phenom- 
enon belongs.  Such  conditions  Mill  called  perma- 
nent causes.  "The  pendulum,  for  example,  has  its 
oscillations  disturbed  by  the  vicinity  of  a  mountain." 
What,  in  such  a  case,  can  be  done  to  make  the 
Method  applicable?  It  is  evident  that  we  cannot 
remove  the  mountain,  but,  as  Mill  points  out,  we 
can  take  the  pendulum  to  a  locality  where  the 
mountain's  intereference  is  reduced  to  a  minimum. 
In  this  way,  it  ceases  to  be  an  "influencing  agent," 
and  becomes  merely  a  "co-existing  fact."  When  an 
experiment  cannot  be  removed  outside  the  sphere  of 
the  operation  of  such  permanent  causes,  recourse 
may  be  had  to  the  Method  of  Concomitant  Variations 
which  is  discussed  below. 

The  Joint  Method  of  Agreement  and  Difference. 
There  is,  no  doubt,  something  ideal  in  the  require- 
ments that  are  laid  down  as  conditions  of  the  use  of 
the  Methods  of  Agreement  and  of  Difference.  It  is 
rarely  that  in  the  course  of  common  life  or  scientific 
investigation  a  number  of  instances  are  given  which 


MILL'S  EXPERIMENTAL   METHODS  487 

agree  or  differ  in  only  a  single  instance.  There 
seems  to  be,  therefore,  a  breach  between  experience, 
on  the  one  hand,  and  these  modes  of  establishing 
causal  relations,  on  the  other.  Either,  then,  we 
shall  have  to  say  that  the  Methods  of  Agreement 
and  of  Difference  are  of  only  limited  application, 
and  that  causal  connections  cannot  be  established 
in  a  great  deal  of  our  experience,  or  that,  with  re- 
spect to  that  part  of  experience  which  does  not  come 
directly  within  the  scope  of  these  Methods,  some 
other  means  of  determining  causal  connections  must 
be  used.  It  is  to  meet  the  latter  of  these  alternatives 
that  the  Joint  Method  of  Agreement  and  Difference 
is  particularly  useful.  The  formulation  of  this 
Method  by  Mill  was  made  necessary  in  view  of  the 
fact,  as  he  says,  that  there  are  "many  cases  in  which, 
though  our  power  of  producing  the  phenomenon  is 
complete,  the  Method  of  Difference  either  cannot  be 
made  available  at  all,  or  not  without  a  previous  em- 
ployment of  the  Method  of  Agreement.  This  occurs," 
says  Mill,  "when  the  agency  by  which  we  can  pro- 
duce the  phenomenon  is  not  that  of  one  single  ante- 
cedent, but  a  combination  of  antecedents,  which  we 
have  no  power  of  separating  from  each  other  and  ex- 
hibiting apart."  Besides  those  cases  in  the  natural 
sciences  which  Mill  had  in  mind,  the  Joint  Method 
will  be  found  applicable,  as  Creighton  has  pointed 
out,  when  we  try  "to  reach  generalizations  regard- 
ing the  behaviour  of  human  individuals  or  human 
societies  —  in  looking  for  moral,  or  social  or  eco- 
nomic laws." 


488 


A  TEXT-BOOK  OF  LOGIC 


The  Joint  Method  is  formulated  by  Mill  as  fol- 
lows: If  two  or  more  instances  in  which  the  phe- 
nomenon occurs  have  only  one  circumstance  in  com- 
mon, while  two  or  more  instances  in  which  it  does 
not  occur  have  nothing  in  common  save  the  absence 
of  that  circumstance,  the  circumstance  in  which  alone 
the  two  sets  of  instances  differ  is  the  effect,  or  the 
cause,  or  an  indispensable  part  of  the  cause,  of  the 
phenomenon.  Thus,  we  are  concerned,  in  this 
Method,  with  two  sets  of  instances,  one  set  of  posi- 
tive instances,  in  which  thei  phenomenon  with  its 
suspected  cause  is  present,  and  one  of  negative 
instances,  in  which  the  phenomenon  with  its  sus- 
pected cause  is  absent.  When  these  conditions  are 
satisfied,  the  Method  affirms  that  the  circumstances 
in  which  the  two  sets  of  instances  differ  is  causally 
connected  with  the  phenomenon.  Let  us  suppose, 
for  example,  that  two  sets  of  instances,  positive  and 
negative,  can  be,  schematically,  analysed  as  follows : 


Antecedents 


POSITIVE   INSTANCES 

ABCD  xyzw 

x  y  v  u 


A  B  E  F 
A  C  F  G 


X    Z    U     t 


Consequents 


Antecedents 


NEGATIVE  INSTANCES 

B  C  D  E  y  z 

C  F  G  H  z 

E  H  J  K  v 


z  w  vl 
u  t  s  L 
s  r  qj 


Consequents 


A  comparison  of  these  instances  shows  that  when 
x  is  present  A  is  present,'  and  that  when  x  is  absent 


MILL'S  EXPERIMENTAL   METHODS  489 

A  is  absent,  and  this  suggests  that  A  and  x  are 
causally  connected.  But  we  cannot  prove  this  by 
the  Method  of  Agreement,  because  there  are  no  two 
instances  which  agree  in  having  only  a  single  cir- 
cumstance is  common;  and  we  cannot  prove  it  by 
the  Method  of  Difference,  because  there  are  no  two 
instances  which  differ  in  no  respect  except  in  the 
presence  of  A  and  x  in  the  positive  instances,  and 
their  absence  in  the  negative  ones.  Moreover,  it 
will  be  observed  that  the  instances  supposed  do  not 
conform  strictly  to  the  requirements  of  Mill's  state- 
ment, and  that  it  is  exactly  this  divergence  that  sets 
the  problem  which  this  Method  is  intended  to  solve. 
In  other  words,  the  agreements  and  differences  are 
greater  in  the  instances  we  have  supposed  than  they 
have  any  right  to  be  on  a  strict  interpretation  of 
Mill's  statement.  The  reason  for  this  divergence  is 
that  Mill's  statement  of  the  Method,  as  Mellone 
remarks,  "is  vague,  and  it  is  incorrect  in  more  than 
one  point;  two  positive  instances  would  never  be 
enough,  still  less  could  two  negative  instances ;  and  it 
is  not  necessary  that  the  negative  instances  should 
have  'nothing  in  common',"  and,  as  our  illustration 
shows,  it  is  not  necessary  that  the  positive  instances 
should  agree  in  only  a  single  circumstance.  With 
these  amendments  in  view,  we  may  quote  Mellone's 
proposed  formulation  of  the  Method :  Whatever  is 
present  in  numerous  observed  instances  of  the  pres- 
ence of  the  phenomenon,  and  absent  in  observed 
instances  of  its  absence,  is  probably  connected  caus- 
ally with  the  phenomenon. 


490  A  TEXT-BOOK  OF  LOGIC 

How,  now,  can  we  proceed  to  apply  the  Method? 
If  we  examine  the  positive  instances,  employing  for 
that  purpose  the  general  principle  of  the  Method 
of  Agreement,  we  shall  see  that  in  the  first  two 
cases  A  or  B  or  AB  is  the  cause  of  the  phenomenon 
x,  since  A  and  B  are  the  only  conditions  present  in 
both.  For  a  similar  reason,  we  see  that  A  or  C  or 
AC  is  the  probable  cause  of  the  phenomenon  in  the 
first  and  third  cases;  and  that  the  cause  in  the 
second  and  third  cases  is  probably  A.  Now  if  the 
probable  cause  in  all  these  instances  is  the  same,  that 
cause  must  be  A,  since  that  is  the  only  particular  in 
which  they  all  agree.  If,  now,  we  examine  the  neg- 
ative instances,  employing  for  that  purpose  the  gen- 
eral principle  of  the  Method  of  Difference,  we  note 
that  they  all  agree  in  the  absence  of  A  and  x,  and 
that  this  is  the  only  relevant  circumstance  in  which 
they  do  agree.  The  absence  in  the  negative  instances 
of  the  supposed  cause  of  x  along  with  the  absence  of 
x,  when  taken  in  connection  with  the  relative 
unimportance  of  the  other  circumstances,  greatly 
strengthens  the  supposition  that  was  reached  as  the 
result  of  examining  the  positive  instance,  namely, 
that  A  is  the  cause  of  x.  Such  a  Method  as  the  one 
here  outlined  has  been  called  by  various  names.  Mill 
spoke  of  it  sometimes  as  "a  double  employment  of  the 
Method  of  Agreement,"  whence  it  is  often  called  the 
Method  of  Double  Agreement.  Mill  also  spoke  of  it 
as  the  Indirect  Method  of  Difference.  But  the  name 
by  which  it  is  commonly  known  is  the  Joint  Method 


MILL'S  EXPERIMENTAL   METHODS  491 

of  Agreement  and  Difference,  a  name  which  Mill 
also  used  in  referring  to  the  method. 

The  following  application  of  the  Joint  Method 
to  a  social  problem  illustrates  so  well,  not  only  its 
usefulness  in  this  class  of  problem,  but  the  nature 
of  the  Method  itself,  that  we  shall  quote  it  entire. 
"We  may  suppose,"  Creighton  writes,  "that  in  a 
certain  part  of  the  country  it  was  noticed  that  a 
considerable  difference  existed  in  the  number  of 
criminal  offenses  committed,  in  proportion  to  the 
number  of  inhabitants,  in  the  various  towns.  In 
several  towns  the  percentage  was  high,  while  in 
others  it  was  relatively  small.  This  being  so,  a 
question  naturally  arose  as  to  the  cause  of  the  high 
percentage.  Now  there  were  among  the  people 
various  opinions  concerning  the  matter.  .  .  .  Not 
being  able  to  agree  about  the  matter,  it  was  decided 
to  appoint  a  committee  to  investigate  the  circum- 
stances existing  in  various  towns  where  the  same 
general  conditions  prevailed,  and  upon  the  basis  of 
this  comparison  to  decide.  The  towns  with  a  high 
criminal  percentage  were  examined  first.  The  re- 
port of  conditions  there  was  as  follows : 

Town  A:  Small  police  force — efficient  schools — severe  pen- 
alties— inactive  churches — licensed  saloon. 

Town  B:  Small  police  force — efficient  schools — light  penal- 
ties— active  churches — licensed  saloons. 

Town  C :  Large  police  force — inefficient  schools — severe  pen- 
alties— active  churches — licensed  saloons. 

Town  D:  Large  police  force — inefficient  schools — light  pen- 
alties— inactive  churches — licensed  saloons. 


492  A  TEXT-BOOK  OF  LOGIC 

"This  report  revealed  the  fact  that  in  each  of 
these  towns  having  a  high  criminal  percentage  there 
was  one  circumstance,  and  only  one,  invariably 
present,  —  the  licensed  saloon.  This  rendered  it 
probable  that  the  saloon  was  the  cause  of  the  high 
percentage  of  crime.  Still,  before  finally  deciding, 
it  was  thought  well  to  investigate  negative  instances 
as  well ;  that  is,  towns  in  which  the  high  percentage 
of  crime  did  not  occur.  The  report  of  conditions 
there  was  as  follows: 

/ 

Town  E:  Large  police  force — efficient  schools — light  penal- 
ties— active  churches — no  licensed  saloons. 

Town  F:  Large  police  force — inefficient  schools — light  pen- 
alties— active  churches — no  licensed  saloons. 

Town  G:  Small  police  force — efficient  schools — light  penal- 
ties— inactive  churches — no  licensed  saloons. 

Town  H :  Small  police  force — inefficient  schools — severe  pen- 
alties— active  churches — no  licensed  saloons. 

"This  table  showed  that  in  the  absence  of  the 
phenomenon  (high  criminal  percentage)  one  and 
only  one  of  the  conditions  concerned  was  invariably 
absent ;  namely,  the  licensed  saloon.  This  confirmed 
the  previous  report  and  established  to  the  satisfac- 
tion of  all  that  the  saloon  was,  at  least,  the  main 
cause  of  the  high  criminal  percentage  in  the  cities 
concerned." 

The  Method  of  Concomitant  Variations.  Mill 
states  this  Method  as  follows :  Whatever  phenom- 
enon varies  in  any  manner  whenever  another  phe- 
nomenon varies  in  some  particular  manner,  is  either 


MILL'S  EXPERIMENTAL   METHODS  493 

a  cause  or  an  effect  of  that  phenomenon,  or  is  con- 
nected with  it  through  some  fact  of  causation.  The 
Method  presupposes  two  classes  of  cases.  Whenever, 
for  example,  any  variation  in  one  phenomenon  ac- 
companies a  variation  in  another,  these  phenomena 
may  either  be  related  directly  as  cause  and  effect, 
or  they  may  be  "two  different  effects  of  a  common 
cause."  The  Method  itself,  however,  does  not  enable 
us  to  decide,  in  any  particular  instance,  which  of 
these  alternative  possibilities  is  realised.  In  order 
to  decide  that  point,  as  Mill  says,  we  should  have  to 
determine  whether  one  set  of  the  variations  in  ques- 
tion were  capable  of  being  produced  by  means  of  the 
other.  In  that  case,  the  relation  is  one  of  cause  and 
effect.  If,  on  the  other  hand,  the  variations  in  ques- 
tion were  not  capable  of  being  produced  in  the  man- 
ner indicated,  we  should  have  to  regard  them  as 
effects  of  a  cause  that  is  common  to  both.  In  both 
cases  the  principle  on  which  the  Method  rests  is 
that  "anything  on  whose  modifications,  modifica- 
tions of  an  effect  are  invariably  consequent,  must 
be  the  cause  (or  connected  with  the  cause)  of  that 
effect,"  As  an  example,  "let  us  suppose,"  to  quote 
Gibson,  "that  an  electric  bell  is  placed  ringing  under 
the  receiver  of  an  air-pump.  The  air  is  now  grad- 
ually exhausted,  and  it  is  noticed  that,  parri  passu 
with  the  exhaustion  of  the  air,  the  sound  of  the 
bell  grows  fainter  and  fainter,  until  a  point  is 
reached  at  which  it  is  no  longer  heard  at  all.  The 
air  is  now  allowed  to  pass  back  gradually  into  the 
receiver,  and,  as  it  does  so,  the  sound  of  the  bell  is 
heard,  at  first  faintly,  then  more  and  more  loudly, 


494  A  TEXT-BOOK  OF  LOGIC 

until  the  clearness  of  the  original  note  is  repro- 
duced." 

The  Method  of  Concomitant  Variations,  as  Mill 
himself  indicated,  is  applicable  particularly  to  those 
cases  in  which  the  Method  of  Difference,  on  account 
of  the  impossibility  of  removing  the  phenomenon 
under  observation  from  the  influence  of  permanent 
causes,  entirely  fails.  Let  us  suppose,  to  take  one 
of  Mill's  illustrations,  that  we  wished  to  know  what 
influence  the  moon  exerts  on  the  surface  of  the 
earth.  "We  cannot  try  an  experiment  in  the  absence 
of  the  moon,  so  as  to  observe  what  terrestrial  phe- 
nomena her  annihilation  would  put  an  end  to;  but 
when  we  find  that  all  the  variations  in  the  position 
of  the  moon  are  followed  by  corresponding  varia- 
tions in  the  time  and  place  of  high  water,  the  place 
being  always  either  the  part  of  the  earth  which  is 
nearest  to,  or  that  which  is  most  remote  from,  the 
moon,  we  have  ample  evidence  that  the  moon  is, 
wholly  or  partially,  the  cause  which  determines  the 
tides." 

Sometimes  it  is  not  the  mere  concomitance 
of  varying  phenomena,  but  the  varying  quantities 
of  the  associated  phenomena,  that  leads  to  the  deter- 
mination of  a  causal  relation  between  these  phenom- 
ena. If,  for  example,  a  connection  between  heat  and 
expansion  is  suspected,  we  can  increase  or  diminish 
the  amount  of  heat,  and  observe  whether,  under 
the  varying  conditions,  any  corresponding  varia- 
tions occur  in  the  expansions  of  a  heated  body.  That 
increase  of  heat  is  followed  by  increased  expansion, 
and  decreased  heat  is  followed  by  decreased  expan- 


MILL'S  EXPERIMENTAL   METHODS  495 

sion,  is  all  the  evidence  we  need  that  there  is  a 
causal  connection  between  the  two  occurrences.  It 
is  by  the  use  of  a  method  such  as  this  in  cases  like 
the  last  that  precise  quantitative  variations  between 
phenomena  may  often  be  made  out.  We  may,  that 
is  to  say,  measure  the  increases  and  decreases  in 
amounts  of  accompanying  phenomena,  and  deter- 
mine the  exact  correlation  between  them.  Some- 
times only  one  of  the  quantities  can  be  measured, 
as,  for  instance,  the  correlation  between  the  inten- 
sity of  a  stimulus  and  the  resulting  sensation  which 
is  formulated  in  what  is  known  as  Weber's  law. 
Whenever  we  experiment  with  variations  of  quantity 
in  accompanying  phenomena,  it  should  be  observed, 
in  general,  that  the  greater  the  number  and  variety 
of  the  instances  in  which  the  correlation  is  known 
to  hold,  the  greater  the  certainty  that  attaches  to  a 
given  conclusion.  The  desirability  of  extending  our 
observation  of  accompanying  variable  phenomena 
over  a  considerable  range  of  instances  is  further 
emphasised  by  the  fact  that  only  in  this  way  can 
we  determine  the  limits  within  which  their  correla- 
tion holds  good.  In  this  way,  for  example,  the  upper 
and  lower  limits  of  the  correlation  between  intensity 
of  stimulus  and  sensation  in  each  of  the  sense  fields 
has  been  ascertained.  Beyond  these  limits,  the  cor- 
relation no  longer  holds  good  either  because  the  phe- 
nomenon changes  its  character  or  ceases  altogether. 
Notwithstanding  the  necessity  for  exercising  care 
in  the  use  of  this  Method,  it  is  particularly  service- 
able in  those  cases  in  which  the  amounts  of  varia- 


496  A  TEXT-BOOK  OF  LOGIC 

tion  can  be  measured.  "Although,"  as  Mill  re- 
marks, "the  most  striking  applications  of  the 
Method  of  Concomitant  Variations  takes  place  in 
the  cases  in  which  the  Method  of  Difference,  strictly 
so  called,  is  impossible,  its  use  is  not  confined  to 
those  cases;  it  may  often  usefully  follow  after  the 
Method  of  Difference,  to  give  additional  precision 
to  a  solution  which  that  has  found.  When  by  the 
Method  of  Difference  it  has  first  been  ascertained 
that  a  certain  object  produces  a  certain  effect,  the 
Method  of  Concomitant  Variations  may  be  usefully 
called  in  to  determine  according  to  what  law  the 
quantity  or  the  different  relations  of  the  effect  fol- 
low those  of  the  cause." 

The  Method  of  Residues.  Most  of  the  phenomena 
with  which  the  sciences  have  to  deal  are  complex. 
The  experimental  methods,  as  they  have  been  for- 
mulated by  Mill,  are,  as  we  have  seen,  statements 
of  ways  that  have  been  devised  for  the  purpose  of 
analysing  various  kinds  and  degrees  of  complexity 
in  the  material  facts  that  constitute  the  subject- 
matter  of  the  particular  sciences.  We  have  seen 
that  when  particular  phenomena  do  not  conform  to 
the  requirements  of  either  of  the  fundamental 
Methods  of  Agreement  or  of  Difference,  the  joint  use 
of  these  Methods  is  then  often  necessary  if  we  are 
to  determine  whether  and,  if  so,  in  what  respects, 
phenomena  are  causally  connected.  Sometimes  our 
analysis  of  phenomena  by  this  Method  enables  us 
merely  to  show  that  complexes  are  probably  con- 


MILL'S  EXPERIMENTAL   METHODS  497 

nected  together  in  a  causal  way.    We  may  find,  for 
example,  in  the  series  of  instances: 


POSITIVE   INSTANCES 


fA  B  C  D  x  y  z  wl 

Antecedents  J  i  Consequents 

[A  B  E  F  x  y  v  uj 

NEGATIVE  INSTANCES 

{BCDE  yzwu] 

)•  Consequents 
CFGH  zutsj 

that  the  negative  instances  confirm  what  the  positive 
instances  suggest,  namely,  that  AB  and  xy  are,  in  all 
probability,  causally  related.  But  the  Method  itself 
does  not,  in  this  case,  enable  us  to  analyse  the  phe- 
nomenon further  to  determine  whether  A  is  causally 
connected  with  x  or  not.  If,  however,  we  supple- 
ment the  Joint  Method  by  the  Method  of  Concom- 
itant Variations,  we  may  be  able,  by  varying  A 
or  x,  to  ascertain  whether  the  two  phenomena 
are  related  as  cause  and  effect.  It  is  obvious, 
further,  that  we  may  employ  the  same  Method 
for  the  purpose  of  ascertaining  whether,  in  the 
above  instances,  B  is  causally  connected  with  y, 
and  C  with  z.  Now,  if  experiment  should  show 
that  A  and  x,  B  and  y,  C  and  z  are  causally  connected 
then,  the  Method  of  Residues,  which  we  have  to 
discuss,  assures  us  that  the  remaining  phenomena, 
namely  D  and  w,  are  also  causally  connected.  Thus, 

32 


498  A  TEXT-BOOK  OF  LOGIC 

the  Method  virtually  says  that  any  remainder  which 
is  left  over  after  other  portions  of  a  complex  phe- 
nomenon have  been  explained,  are  themselves 
causally  connected.  Mill's  statement  is  as  follows: 
Subduct  from  any  phenomenon  such  part  as  is  known 
by  previous  inductions  to  be  the  effect  of  certain  ante- 
cedents, and  the  residue  of  the  phenomenon  is  the 
effect  if  the  remaining  antecedents. 

The  Method  of  Residues,  as  it  has  just  been 
stated,  is  constantly  employed  in  the  sciences.  To 
take  one  illustration  only,  as  this  is  given  by  Jevons. 
"In  chemical  analysis,"  he  writes,  "this  method  is 
constantly  employed  to  determine  the  proportional 
weight  of  substances  which  combine  together.  Thus 
the  composition  of  water  is  ascertained  by  taking 
a  known  weight  of  oxide  of  copper,  passing  hydro- 
gen over  it  in  a  heated  tube,  and  condensing  the 
water  produced  in  a  tube  containing  sulphuric  acid. 
If  we  subtract  the  original  weight  of  the  condensing 
tube  from  its  final  weight,  we  learn  how  much  water 
is  produced;  the  quantity  of  oxygen  in  it  is  found 
by  subtracting  the  final  weight  of  the  oxide  of 
copper  from  its  original  weight.  If  we  then  sub- 
tract the  weight  of  the  oxygen  from  that  of  the 
water,  we  learn  the  weight  of  the  hydrogen  which 
we  have  combined  with  the  oxygen.  When  the 
experiment  is  carefully  performed  ...  we  find  that 
88.9  parts  by  weight  of  oxygen  unite  with  11.11 
parts  of  hydrogen  to  form  100  parts  of  water." 

Mill  calls  our  attention  to  the  fact  that  the 
Method  of  Residues  is  specially  serviceable  in  those 


MILL'S  EXPERIMENTAL   METHODS  499 

cases  where  several  causes  acting  together  produce 
an  effect  which  is  the  joint  result  of  all  the  causes 
taken  together.  In  such  cases,  we  have,  what  Mill 
calls,  an  "intermixture  of  effects."  What  is  meant 
by  an  intermixture  of  effect  has  been  explained  by 
Jevons  as  follows:  "If  in  one  experiment  friction, 
combustion,  compression,  and  electric  action  are  all 
going  on  at  once,  each  of  these  causes  will  produce 
quantities  of  heat  which  will  be  added  together,  and 
it  will  be  difficult  or  impossible  to  say  how  much 
is  due  to  each  cause  separately.  We  may  call  this 
a  case  of  the  homogeneous  intermixture  of  effects, 
the  name  indicating  that  the  joint  effect  is  of  the 
same  kind  as  the  separate  effects.  There  are  several 
causes,  each  producing  a  part  of  the  effect,  and  we 
want  to  know  how  much  is  due  each."  What  is  here 
called  by  Jevons  a  homogeneous  intermixture  of 
effects,  Mill  also  called  a  Composition  of  Causes.  He 
writes :  "I  shall  give  the  name  of  the  Composition 
of  Causes  to  the  principle  which  is  exemplified  in 
all  cases  in  which  the  joint  effect  of  several  causes 
is  identical  with  the  sum  of  their  separate  effects." 
In  contradistinction  to  the  case  just  mentioned,  the 
intermixture  of  effects  may  also  be  heterogeneous 
when,  as  Mill  says,  "the  agencies  which  are  brought 
together  cease  entirely,  and  a  different  set  of  phe- 
nomena arise:  as  in  the  experiment  of  two  liquids 
which,  when  mixed  in  certain  proportions,  instantly 
become,  not  a  larger  amount  of  liquid,  but  a  solid 


500  A  TEXT-BOOK  OF  LOGIC 

We  may  remark,  further,  that  the  Method  of 
Residues  is  significant  because  it  operates  in  the 
interests  of  thoroughness  in  scientific  observation. 
It  sets  a  barrier  against  carrying  over  into  science 
the  popular  attitude  towards  what  is  small  and 
insignficant,  and  its  use  has  taught  the  scientist 
that  what  appears  small  and  insignficant  if  often 
the  hinge  upon  which  scientific  discoveries  of  the 
first  important  turn.  "Almost  all  the  greatest  dis- 
coveries in  astronomy,"  says  Herschel,  "have  re- 
sulted from  the  consideration  of  residual  phenomena 
of  a  quantitative  or  numerical  kind.  .  .  It  was  thus 
that  the  grand  discovery  of  the  Procession  of  the 
Equinoxes  resulted  as  a  residual  phenomenon,  from 
the  imperfect  explanation  of  the  return  of  the  sea- 
sons by  the  return  of  the  sun  to  the  same  apparent 
place  among  the  fixed  stars."  The  discovery  of  the 
planet  Uranus,  to  which  we  have  referred  in  an- 
other connection,  and  the  invention  of  the  steam 
engine,  are  other  instances  of  the  importance  of 
paying  attention  to  residual  phenomena.  What  one 
calls  'luck'  in  ordinary  life,  what  one  calls  'genius' 
in  scientific  life,  and  what  one  calls  'success*  in 
commercial  life  are  all  of  them  very  often  merely 
the  result  of  giving  heed  to  details  that  the  average 
person  passes  lightly  by.  In  this  regard,  the  fol- 
lowing quotation  from  Darwin's  'Life  and  Letters' 
has  its  value.  "A  point  apparently  slight  and  un- 
connected with  his  present  work  is  passed  over  by 
many  a  man  almost  unconsciously,  with  some  half- 
considered  explanation,  which  is  really  no  explana- 


MILL'S  EXPERIMENTAL   METHODS  501 

tion.     It  was  just  these  things  that  he   (Darwin) 
seized  upon  to  make  a  start." 

REFERENCES 

H.  A.  Aikins,  The  Principles  of  Logic,  Chs.  XXVI.,  XXVII., 
XXIX. 

J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Chs. 
XVI.,  XVII. 

S.  H.  Mellone,  An  Introductory  Text-Book  of  Logic,  3d  Edi- 
tion, Ch.  IX.,  §§3-9. 

W.  Minto,  Logic,  Inductive  and  Deductive,  Book  II.,  Chs.  IV., 
V.,  VI. 

C.  Read,   Logic,   Deductive  and   Inductive,  3d   Edition,   Ch. 

XVI. 

ADVANCED 

W.  R.  B.  Gibson,  The  Problem  of  Logic,  Ch.  XLV. 
L.  T.  Hobhouse,  The  Theory  of  Knowledge,  Chs.  XIII.,  XIV., 
XV. 

D.  Hume,  Treatise  of  Human  Nature,  Book  I.,  Part  III.,  §  XV. 
H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Ch.  XX. 

H.  Lotze,  Logic,  Book  II.,  Ch.  VII. 

J.  S.  Mill,  A  System  of  Logic,  Book  III.,  Chs.  VIII.,  IX. 

C.  Sigwart,  Logic,  Vol.  II.,  Part  III.,  Ch.  V., 


QUESTIONS 

1.  State  briefly  the  relation  of  Mill's  'Logic'  to  the  history 
of  inductive  logic  in  the  modern  era. 

2.  With  what  problem  does  Mill's  chapter  on  'The  Four 
Methods  of  Experimental  Inquiry'  deal? 

3.  What  is  meant  by  calling  causal  relations  reciprocal? 

4.  Are  all  causal  relations  reciprocal?    Explain. 

5.  What  relation  have  Mill's  Methods  to  the  special  modes 
of  inquiry  developed  by  each  science  to  meet  its  own 
problems? 


502  A  TEXT-BOOK  OF  LOGIC 

6.  Explain  as  well  as  you  can  exactly  what  Mill's  Methods 
undertake  to  do. 

7.  In  what  sense  can  it  be  said  that  Mill's  Methods  rest 
upon  a  process  of  elimination? 

8.  What   is   Joseph's   view   of   elimination   as   applied   to 
causal  problems? 

9.  What  view,  according  to  Gibson,  does  Mill  take  of  the 
nature  of  elimination? 

10.  What  is  the  characteristic  feature  of  the  Method  of 
Agreement? 

11.  What  is  Jevons'  formulation  of  Mill's  Method  of  Agree- 
ment? 

12.  What  criticisms  may  be  passed  on  this  Method  for  de- 
manding a  point  of  single  agreement  among  the  phe- 
nomena which  it  examines? 

13.  Is   the   Method   of   Agreement   one   of   observation   or 
explanation?     Give  reasons  for  your  answer. 

14.  What  degree  of  certinty  attaches   to  the  conclusions 
reached  by  the  Method  of  Agreement? 

15.  What  are  the  chief  features  of  the  Method  of  Differ- 
ence as  formulated  by  Mill? 

16.  What  is  meant  by  calling  the  Method  of  Difference  a 
method  of  scientific  experiment? 

17.  How  does  Mellone  formulate  the  Method  of  Difference? 

18.  What  two  kinds  of  instances  are  presupposed  by  the 
Method   of  Difference,   and   by  what   names   are  they 
called? 

19.  Why  is  it  necessary  to  vary  only  one  condition  at  a  time 
in  a  series  of  scieintific  experiments? 

20.  What  does  Mill  mean  by  a  permanent  cause? 

21.  How  does  the  operation  of  permanent  causes  affect  the 
applicability  of  the  Method  of  Difference? 

22.  Under  what  conditions  does  the  Joint  Method  of  Agree- 
ment and  Difference  become  effective? 

23.  To  what  two  classes  of  problems  is  the  Joint  Method 
applicable? 


MILL'S  EXPERIMENTAL   METHODS  503 

24.  What  are  the  chief  features  of  the  Joint  Method  as 
formulated  by  Mills? 

25.  Show,   by   the   enumeration    of   supposed    instances    to 
which  the  Methods  of  Agreement  and  of  Difference  do 
not  apply,  the  conditions  which  call  for  the  use  of  the 
Joint  Method. 

26.  What  criticism  can  be  made  of  the  way  in  which  Mill 
formulates  the  Joint  Method? 

27.  What   statement   has   been   given   by    Mellone   of   this 
Method  so  as  to  avoid  such  criticism? 

28.  Explain  carefully  and  in  detail  how  you  would  apply  the 
Joint  Method. 

29.  Verify  each  step  of  your  answer  to  the  previous  ques- 
tion by  using  the  analysis  of  the  social  example  given 
in  the  text. 

30.  What  is  the  Method  of  Concomitant  Variations? 

31.  What  two  classes  of  cases  are  presupposed  by  Mill's 
statement  of  the  Method  of  Concomitant  Variations? 

32.  How  can  you  determine  which  of  these  two  cases  is 
present  in  any  particular  instance? 

33.  On  what  general  principle  does  the  Method  of  Concom- 
itant Variations  rest? 

34.  What  is  the  relation  of  this  Method  to  that  of  Differ- 
ence?   How  is  it  affected  by  the  operation  of  permanent 
causes? 

35.  In  what  way  does  the  Method  of  Concomitant  Variations 
enable  us  to  determine  causal  relations  between  quan- 
titative phenomena? 

37.  Illustrate  how  the  measurements  of  quantitative  phe- 
nomena enable  us  to  determine  causal  relations,  first, 
in  instances  where  both  antecedent  and  consequent  can 
be  measured,  and,  second,  where  only  antecedent  can  be. 

38.  What,    according   to    Mill,    are   the   chief   uses    of   the 
Method  of  Concomitant  Variations? 


504  A  TEXT-BOOK  OF  LOGIC 

39.  State  briefly  the  relations  of  the  Methods  of  Agreement 
and  Differences,  the  Joint  Method,  and  the  Method  of 
Concomitant  Variations  to  one  another  with  a  view  to 
shrow  what  Mill  means  by  the  Method  of  Residues. 

40.  Illustrate  the  Method  of  Residues. 

41.  What  does  Mill  mean  by  the  intermixture  of  effects? 

42.  Why  should  the  Method  of  Residues  be  specially  applic- 
able to  cases  which  involve  an  intermixture  of  effects? 

43.  In  what  way  does  the  Method  of  Residues  operate  in 
the  interests  of  thoroughness  in  scientific  observation? 

EXERCISES 

1.  Examine  each  of  the  examples  of  inductive  reasoning 
given  below,  and  state  by  what  method  or  combination 
of  methods  the  conclusion  in  each  case  is  reached. 

(1)  It  is  found  that  sun-lit  air  has  been  the  means  of 
eliminating  some  diseases,  and  of  diminishing  the 
severity  of  a  number  of  others;  whence  it  seems 
to  follow  that  for  maintaining  a  high  degree  of 
health  sun-light  air  is  essential. 

(2)  Other  conditions  remaining  the  same,  children  who 
are  taught  in  classes  which  average  from  twenty 
to  twenty-five  in  number  attain  in  the  same  amount 
of  time  a  higher  degree  of  proficiency  than  those 
taught  in  classes  which  average  from  forty  to  fifty, 
or    attain    the    same    degree    of   proficiency   in    a 
shorter  amount  of  time. 

(3)  Sachs  maintained,  in  1862,  that  starch  is  formed 
by    the    decomposition    in    chlorophyl    of    carbon- 
dioxide  gas  under  the  influence  of  light.    He  found 
that  when  all  other  conditions  were  constant,  and 
light  was  excluded   from  a  plant,  no  starch  was 
formed;    the    single   circumstance    of   readmitting 
light  was  accompanied  by  renewed   formation  of 
starch.    Further,  he  found  that  if  certain  portions 


MILL'S  EXPERIMENTAL   METHODS  505 

of  the  leaves  of  an  illuminated  plant  were  covered 
with  black  paper,  no  starch  was  found  in  these 
portions. 

(4)  Tyndall  found  that  of  twenty-seven  sterilised  flasks 
containing  infusion  of  organic  matter,  and  opened 
in  pure  Alpine  air,  not  one  showed  putrefaction; 
while  of  twenty-three  similar  flasks,  opened  in  a 
hay  loft,  only  two  remained  free  from  putrefaction 
in  three  days.     He  concluded  that  putrefaction  is 
due  to  floating  particles  in  the  air. 

(5)  In  1675  Leeuwenhoek  discovered  infusoria,  or  ani- 
malculae  under  the  microscope,  and  it  was  thought 
that   such   minute   organisms    as   these   might   be 
spontaneously  generated,  even  if  the  larger  were 
not.     About   1745   Needham  performed   a  number 
of  experiment  to  test  this  conclusion.    He  extracted 
the  juices  of  meat  by  boiling,   enclosed  them  in 
bottles,   which   were   carefully   corked    and    sealed 
with  mastic,  then  subjected  the  closed  bottles  to 
heat  and  set  them  away  to  cool.    In  due  course  of 
time,  the  fluids  thus  treated  became  infected  with 
microscopic  life,  and  inasmuch  as  he  believed  that 
he  had  killed  all  living  germs  by  repeated  heating, 
he  concluded  that  the  living  forms  had  been  pro- 
duced by  spontaneous  generation. 

(6)  Spellanzi,   however,    thought   that   Needham 's    ex- 
periments had   not  been  conducted  with  sufficient 
care.    He,  therefore,  made  a  great  number  of  sim- 
ilar experiments,  using  different  kinds  of  infusions. 
But  he  placed  them   in  thin  flasks  with   slender 
necks,    which    were    then    hermetically    sealed    in 
flame,  after  which  he  immersed  the  flasks  in  boil- 
ing water  for  three-quarters  of  an  hour,  in  order 
to  destroy  all  germs  that  might  be  contained  in 
them.     Under   these   conditions   no   infusoria   ap- 


506  A  TEXT-BOOK  OF  LOGIC 

peared  in  them.  Needham  was  not  satisfied  with 
these  results,  however,  and  objected  that  such  pro- 
longed boiling  would  destroy  not  only  germs,  but 
the  generative  force  of  the  infusion  itself.  Spell- 
anzi  easily  disposed  of  this  objection  by  showing 
that  when  the  infusions  were  again  exposed  to  the 
air,  no  matter  how  severe  or  prolonged  the  boiling 
to  which  they  had  been  subjected,  the  infusoria  re- 
appeared. 

(7)  Goldschn eider    proved    that    muscular    sensations 
play  no  considerable  part  in  our  consciousness  of 
the  movement  of  our  limbs,  by  having  his  arm  sus- 
pended in  a  frame  and  moved  by  an  attendant. 
Under   these   circumstances,    where   no    work    de- 
volved on  his  muscles,  he  found  that  he  could  dis- 
tinguish as  small  an  angular  movement  of  the  arm 
as  when  he  moved  and  supported  it  himself. 

(8)  The  case  has  been  supposed  of  a  man  who,  having 
a  taste  for  cucumber,  attributes  his  chronic  indi- 
gestion now  to  the  salmon,  now  to  the  cheese,  now 
to  the  pastry  —  no  one  of  which  is  an  invariable 
feature   of  his   evening  meal  —  but  never  to   the 
cucumber,  which  he  takes  every  evening.    However, 
after  having  dined  without  cucumber  on   several 
consecutive    evenings,    whilst    taking    salmon    one 
evening,  pastry  the  next,  and  so  on  through  the 
whole  list  of  suspicious  dishes,  he  cannot  but  notice 
that  on  no  one  of  these  evenings  did  any  indiges- 
tion occur,  and  is  thus  brought  to  confess  that  the 
cucumber,  after  all,  must  have  been  the  offending 
cause. 

(9)  F«rri,  in  his  Criminal  Sociology,  writes:     I  have 
shown  that  in  France  there  is  a  manifest  corre- 
spondence of  increase   and   decrease  between  the 
number    of    homicides,     assaults    and     malicious 


MILL'S  EXPERIMENTAL  METHODS  507 

wounding,  and  the  more  or  less  aboundant  vintage, 
especially  in  the  years  of  extraordinary  variations, 
whether  of  failure  of  vintage  (1853-5,  1859,  1867, 
1873,  1878-80),  attended  by  a  remarkable  diminu- 
tion of  crime  (assault  and  woundings),  or  of  abun- 
dant vintages  (1850,  1856-8,  1862-3,  1865,  1874-5), 
attended  by  an  increase  of  crime. 


CHAPTER  XVIII 

FALLACIES 

Fallacy  Defined.     The  earliest  systematic  account 
of  fallicies  was  given  by  Aristotle  in  his  treatise 

Was  On  sophistical  arguments   (-n-epl  O-O^HO-TIKWJ/  eAeyx^)- 

The  aim  of  this  treatise  was  to  name  and  examine 
the  various  tricks  that  were  relied  on  by  many  of 
the  sophists  to  win  the  applause  of  their  audience. 
We  may  say,  therefore,  that  it  contains  an  exami- 
nation of  the  various  forms  of  'sophistry'  current 
among  the  Greeks  of  the  fourth  century  B.  C.  To 
this  practical  employment  of  the  term  corresponds, 
in  a  general  way,  the  meaning  that  must  be  assigned 
to  it  when,  at  the  present  day,  it  is  used  in  a  popular 
sense.  From  this  point  of  view,  a  fallacy  may  be 
said  to  be  any  error  of  statement  or  belief.  If,  for 
example,  any  one  should  believe  that  the  sun  revolves 
around  the  earth,  such  a  belief  would  be  called  fal- 
lacious, and  the  statement  of  that  belief  would 
be  called  a  fallacy.  This  meaning  of  the  word, 
however,  is  too  indefinite  for  the  purposes  of  logic, 
and  it  covers  too  miscellaneous  a  group  of  cases  to 
be  of  much  service  in  directing  its  inquiries.  It 
is  customary,  therefore,  to  narrow  the  interpreta- 
tion of  the  term  by  confining  its  application  to  any 
breach  of  the  principles  and  rules  of  logical  pro- 
cedure. In  the  foregoing  pages,  we  have  become 
acquainted  with  a  number  of  the  principles  and 

(508) 


FALLACIES  509 

rules  to  which  we  must  submit  our  thought  and  our 
speech  if  what  we  assert  and  what  we  express  are 
to  carry  logical  conviction.  And,  doubtless,  our 
study  of  these  principles  and  rules,  and  our  effort 
to  put  them  into  practice,  have  convinced  us  both 
of  the  necessity  and  of  the  difficulty  of  conforming 
our  thought  and  speech  to  their  requirements.  Now 
whenever  our  thinking  fails  to  conform  to  such 
principles  and  rules,  we  are  said,  in  the  strict  sense 
in  which  the  term  is  used  in  logic,  to  be  guilty  of  a 
fallacy.  A  fallacy,  therefore,  may  be  defined  as  any 
breach  of  a  logical  principle  or  rule. 

This  statement  of  what  we  understand  in  logic 
by  a  fallacy  needs  to  be  safeguarded  in  one  par- 
ticular. As  it  stands,  and  especially  if  one  does 
not  regard  strictly  the  context  in  which  it  occurs, 
it  will  seem  capable  of  including,  not  only  those 
breaches  of  logical  procedure  to  which  the  definition 
is  intended  to  confine  it,  but  also  those  errors  which 
arise  from  other  than  logical  sources,  and  to  which 
the  term  fallacy  can  be  applied  only  in  a  popular 
and  conventional  sense.  There  are,  no  doubt,  nat- 
ural limitations  of  mind  which  prevent  all  of  us 
at  some  time  from  attaining,  in  the  character  of  our 
intellectual  life,  anything  that  can  be  called  with 
propriety  logical  exactness.  Indeed,  the  ordinary 
course  of  life,  as  we  have  so  often  said,  does  not 
depend  for  the  attainment  of  its  objects  on  the 
strictness  with  which  logical  requirements  are  met 
in  the  field  of  the  interests  by  which  that  life  is 
controlled.  And,  doubtless,  mistakes  occur  here 


510  A  TEXT-BOOK  OP  LOGIC 

which  have  their  roots  in  the  mental  process  by 
means  of  which  that  life  is  carried  on.  We  have 
pointed  out,  for  instance,  that  perception  does  not 
provide  a  secure  foundation  of  knowledge,  and  if 
we  were  to  add  that  the  organisation  of  our  ordi- 
nary experience  proceeds  very  largely  upon  prin- 
ciples of  association,  it  would  be  evident,  in  the 
light  of  our  previous  studies,  that  association  cannot 
guarantee  against  logical  error  the  conclusions  to 
which  it  is  the  means  of  conducting  us.  In  so  far, 
then,  as  we  have  regard  to  the  mistakes  that  arise 
in  this  field,  it  would  be  quite  misleading  to  apply 
the  term  fallacy  to  these  mistakes,  and  they  must 
be  considered  as  falling  outside  the  scope  of  our 
definition.  We  may  point  out  also  that  lapses  into 
this  more  usual  method  of  procedure  are  likely  to 
occur  in  the  course  of  our  efforts  to  reach  more 
strictly  scientific  results.  The  exclusion  of  these 
cases  from  the  field  of  the  fallacies  is  made  on  the 
principle  that  such  cases  do  not  involve  ignorance 
of  the  methods  of  logical  procedure,  but  carelessness 
in  their  application;  just  as,  for  example,  ignorance 
of  a  mathematical  rule  would  not  be  attributed  to 
one  whose  mistake  was  obviously  due  to  haste  or 
inattention  in  its  application  to  a  given  case.  We 
must  regard  as  logical  fallacies,  therefore,  only 
those  instances  of  erroneous  conclusions  which  rest 
upon  grounds  which  are  demonstrably  false.  It  is 
in  this  sense,  then,  that  a  fallacy  was  defined  above 
as  any  breach  of  a  logical  principle  or  rule. 


FALLACIES  511 

Classification  of  Fallacies.  Although  Aristotle 
was  limited  in  his  treatment  of  fallacies  by  the 
practical  purpose  to  which  reference  has  been  made, 
and  although  he  had  before  him  chiefly  those  errors 
to  which  the  Sophists  were  exposed  by  their  desire 
for  popular  favour,  his  classification  of  fallacies 
has  remained  the  basis  of  what  may  be  regarded  in 
logic  as  the  traditional  position  on  this  subject.  In 
the  work  referred  to,  Aristotle  divided  fallacies  into 
two  main  classes,  a  division  which  corresponds,  in  a 
general  way,  to  the  distinction  on  which  we  have  in- 
sisted in  our  discussions  of  logical  doctrine,  the  dis- 
tinction, namely,  between  truth  in  the  form  of  judg- 
ments, and  truth  expressed  in  the  form  of  proposi- 
tions. According  to  this  distinction,  fallacies  may 
arise  from  the  way  in  which  we  express  or  interpret 
propositions,  or,  as  Aristotle  said,  they  may  be  due 
directly  to  language  (napa  T^V  Ae'&v;  in  dictione)  ;  or 
they  may  exist  in  the  thoughts  or  judgments  that 
we  assert,  or,  as  Aristotle  expressed  it  negatively, 
they  may  not  be  due  to  the  language  we  employ 
(e£w  IT/?  Ae'^ews;  extra  dictionem).  Under  the  first 
class  Aristotle  enumerates  six  kinds  of  fallacy,  some 
of  which  are  trifling  and  dependent  wholly  on  the 
syntax  of  the  Greek  language ;  and  under  the  second 
class,  he  enumerates  seven.  Beyond  the  distinction 
of  these  two  main  classes  we  are  not  directly  inter- 
ested in  Aristotle's  classification. 

There  is,  perhaps,  no  entirely  satisfactory  class- 
ification of  fallacies,  and  the  most  that  can  be 
attempted  here  is  to  bring  under  some  practical  and 


512  A  TEXT-BOOK  OF  LOGIC 

intelligible  scheme  the  various  errors  to  which  log- 
ical thinking  is  exposed.  It  will  help  us  to  do  this 
if  we  recall,  in  the  first  place,  that  the  proposition 
was  said  to  be  an  expression  in  words  of  the  truth 
asserted  in  a  judgment.  We  saw  that,  for  the  per- 
son speaking,  the  problem  was  to  find  words  which 
express  adequately  the  thought  that  he  desires  to 
convey,  and,  for  the  person  spoken  to,  it  was  to 
interpret  the  words  in  which  a  judgment  is  ex- 
pressed in  the  sense  that  they  had  for  the  person 
who  first  used  them  as  the  embodiment  of  an  idea. 
In  either  case,  the  logical  value  of  a  proposition 
depends  to  a  large  extent  on  language,  on  the  fitness 
of  the  verbal  forms  which  are  chosen  as  the  medium 
of  ideas.  If  one  realises  the  great  difficulty,  which 
the  masters  of  literature  alone  have  at  all  adequately 
overcome,  of  choosing  words  that  reveal  the  mean- 
ing their  employment  is  intended  to  convey,  he  will 
understand  why  logicians,  since  Aristotle,  have  con- 
tinued to  regard  language  as  one  main  source  of 
logical  fallacy.  The  study  of  the  fallacies  which 
beset  our  interpretation  of  propositions  through 
the  ambiguous  use  of  language  will  form  for  us  the 
first  group  of  fallacies. 

Our  second  main  group  of  fallacies  will  comprise 
those  mistakes  which  threaten  our  comprehension 
of  the  full  meaning  of  propositions.  It  will  be 
remembered  that  we  pointed  out  that  our  relation 
to  propositions  is  two  fold.  In  the  first  place,  prop- 
ositions need  interpreting,  and,  as  we  have  just  now 
intimated,  the  difficulties  in  the  way  of  interpreting 


FALLACIES  513 

propositions  constitutes  the  first  main  class  of  fal- 
lacies. But,  in  the  second  place,  it  was  pointed  out 
that  propositions  contain  implications  which  limit 
in  certain  determinate  directions  what  we  can  think 
about  the  subject-matter  of  their  assertion.  For 
instance,  we  said  that  if  we  admit  the  truth  or 
falsity  of  a  given  proposition  we  are  thereby  com- 
mitted to  the  truth  or  falsity  of  a  number  of  other 
propositions.  An  examination  of  the  possible 
sources  of  error  in  this  region,  the  region  of  logical 
implication,  will  enable  us  to  avoid  one  of  the  most 
frequent  pitfalls  in  the  way  of  that  accuracy  and 
precision  that  is  the  desideratum  of  the  intellectual 
life. 

The  fallacies  that  are  included  under  the  two 
heads  just  mentioned  refer  to  the  meaning  of  prop- 
ositions taken  singly,  they  are  the  fallacies  which 
arise  in  the  field  of  simple,  unmediated  assertion. 
When,  however,  we  go  beyond  this  region,  and  our 
assertions  take  the  more  complex  forms  that  we 
have  studied  in  the  syllogism  and  induction,  a 
special  group  of  fallacies  has  to  be  recognised,  be- 
cause here  thought  is  guided  in  its  efforts  to  reach 
logically  sound  conclusions  by  special  principles  and 
rules.  The  mistakes  that  occur  in  connection  with 
the  control  of  thought  by  these  principles  and  rules 
will  constitute  a  third  main  group  of  fallacies. 

A  fourth  group  of  fallacies  may  be  recognised 
if  we  recall  that  no  logical  assertion,  whether  simple 
or  complex,  is  ever  a  wholly  detached  unit,  and 

33 


514  A  TEXT-BOOK  OF  LOGIC 

that,  if  such  assertions  are  to  be  interpreted  cor- 
rectly, they  must  be  brought  into  relation  to  the 
contexts  out  of  which  their  original  meaning  was 
forged.  Every  assertion,  we  have  said,  implies  a 
certain  universe  of  discourse.  Now  we  often  find 
that  the  plausibility  of  statements  and  arguments 
depends  on  suggestions  derived  from  their  contexts 
which  are  not  directly  related  to  the  truth  char- 
acter of  the  statements  and  arguments  themselves, 
and  for  these  extrinsic  reasons  are  frequently, 
though  fallaciously,  accepted  as  true.  They  are 
cases  of  this  kind  that  we  shall  classify  under  the 
present  head. 

For  the  sake  of  convenience,  we  shall  refer  to 
the  four  main  classes  of  fallacy  that  have  just  been 
distinguished,  in  the  order  in  which  we  have  con- 
sidered them,  as  fallacies  of  interpretation,  of  im- 
plication, of  inference,  and  of  the  context.  A  cer- 
tain latitude  must  be  allowed  in  the  use  o*f  this 
classification,  as  indeed  it  must  of  any  classification, 
of  fallacies.  The  only  justification  that  any  scheme 
can  receive  is  that  it  brings  together,  in  a  way  that 
connects  with  the  development  of  logical  doctrine, 
the  errors  to  which  we  are  exposed  in  our  efforts 
to  think  accurately  and  convincingly.  If,  in  addi- 
tion, it  groups  the  fallacies  in  a  way  that  is  easily 
remembered,  it  has  a  still  further  advantage. 

Fallacies  of  Interpretation.  These  are  due,  as  we 
have  said,  to  the  deceptiveness  of  the  language  in 
which  propositions  are  expressed.  They  all,  there- 
fore, fall  under  the  defect  of  ambiguity.  But  since 


FALLACIES  515 

ambiguity  may  attach  either  to  the  words  or  to  the 
structure  of  our  statements,  we  may  distinguish 
two  classes  of  error  to  which  our  interpretation  of 
propositions  is  exposed.  Among  the  fallacies  due  to 
verbal  ambiguity  we  may  include  equivocation, 
accent,  composition,  division,  accident,  and  converse 
fallacy  of  accident;  and  among  those  due  to  struc- 
tural ambiguity,  amphibole  and  false  parenthesis. 

Verbal  Ambiguity.  In  discussing  the  fallacies 
that  are  due  to  verbal  ambiguity,  we  may  remind 
ourselves  that  ambiguity  is  not  identical  with  mere 
indefiniteness  in  the  meaning  of  words,  and  that, 
in  view  of  a  certain  unavoidable  indefiniteness  in 
the  meanings  of  the  words  we  employ,  propositions 
can  attain  only  a  non-ambiguous  signification.  The 
principle  of  non-ambiguity,  we  said,  controlled  all 
our  efforts  after  logical  exactness  both  with  respect 
to  terms  and  propositions.  We  cannot,  therefore, 
convict  of  any  of  the  verbal  fallacies  a  proposition 
whose  terms  are  indefinite,  if  this  indefiniteness 
does  not  spread  to  the  meaning  of  the  proposition 
taken  as  a  whole.  When,  however,  the  indefiniteness 
of  the  parts  affects  the  meaning  of  the  whole  prop- 
osition, we  have  a  case  that  falls  under  the  class 
of  fallacies  that  we  are  now  considering.  With  this 
reminder,  we  take  up  seriatim  the  several  fallacies 
that  originate  in  verbal  ambiguity. 

Equivocation,  or  indefiniteness  in  the  denotation 
or  connotation  of  a  term,  gives  rise  to  a  fallacy 
when  either  term  of  a  proposition  is  interpreted  in 
a  different  sense  by  the  speaker  and  by  the  person 


516  A  TEXT-BOOK  OF  LOGIC 

spoken  to,  and  this  affects  the  meaning  of  the  prop- 
osition as  a  whole ;  or  when,  for  the  same  individual, 
any  term  which  appears  in  a  continuous  discourse 
fails  to  retain  the  same  meaning  in  the  various 
propositions  in  which  it  occurs,  and  this  affects 
the  conclusion  to  which  one  is  led.  The  latter  is, 
perhaps,  the  more  usual,  as  it  is,  certainly,  the  more 
insidious,  form  of  the  fallacy  of  equivocation.  Any 
form  of  continuous  address,  and  especially  of  public 
address,  exposes  one  to  the  danger  of  equivocation, 
and  the  most  careful  writers  sometimes  fall  into  it. 
A  familiar  example  is  the  following  taken  from 
Mill's  argument  in  support  of  the  position  that  hap- 
piness is  the  chief  aim  or  good  of  life.  He  says, 
"The  only  proof  capable  of  being  given  that  an 
object  is  visible  is  that  people  actually  see  it.  The 
only  proof  that  a  sound  is  audible  is  that  people 
hear  it.  And  so  of  the  other  sources  of  our  expe- 
rience. In  like  manner,  I  apprehend,  the  sole  evi- 
dence it  is  possible  to  produce  that  anything  is 
desirable  is  that  people  do  actually  desire  it."  For 
the  purpose  of  his  argument,  the  word  desirable 
must  have  the  meaning  'worthy  to  be  desired/  but 
this  is  a  meaning  that  is  not  analogous  to  visible 
and  audible  in  the  context.  Visible  and  audible 
mean  able  to  be  seen  or  heard,  and/  therefore,  all 
that  Mill  has  a  right  to  argue  is  that  desirable 
means  'able  to  be  desired/  But  from  this  meaning 
he  could  not  argue  that  happiness  is  the  summum 
bonum  or  chief  good  of  life,  for  the  fact  that  a 
person  desires  an  object  is  no  proof  that  it  is,  in  the 


FALLACIES  517 

sense  Mill  uses  the  word,  the  most  desirable. 
Against  committing  or  being  imposed  on  by  the 
fallacy  of  equivocation  we  may  submit  the  meanings 
of  our  terms  to  the  methods  of  translation  and  defi- 
nition, as  these  terms  have  been  explained  above. 

Accent.  The  fallacy  of  accent  is  any  misconcep- 
tion due  to  the  emhasis  placed  on  a  word  or  group 
of  words  in  a  sentence.  It  was  for  Aristotle  the 
mistaken  accentuation  of  a  word  in  writing  Greek. 
"A  ludicrous  instance  of  this  fallacy,"  to  quote 
Jevons,  "is  likely  to  occur  in  reading  Chapter  XIII 
of  the  First  Book  of  Kings,  verse  27,  where  it  is 
said  of  the  prophet,  'And  he  spake  to  his  sons,  say- 
ing, Saddle  me  the  ass.  And  they  saddled  him.' 
The  italics  indicate  that  the  word  him  was  supplied 
by  the  translators  of  the  authorised  version,  but  it 
may  suggest  another  meaning.  The  commandment, 
Thou  shalt  not  bear  false  witness  against  thy 
neighbour/  may  be  made  by  a  slight  emphasis  of  the 
voice  on  the  last  word  to  imply  that  we  are  at  liberty 
to  bear  false  witness  against  other  persons."  We 
may,  however,  give  certain  words  or  groups  of  words 
a  prominence  that  does  not  really  belong  to  them  in 
another  way.  For  example,  in  quoting  an  author 
we  may  separate  a  word  from  its  context,  italicise 
a  word  which  was  not  italicised  in  the  original,  or, 
by  leaving  out  qualifying  words  and  phrases,  we 
may  give  certain  ideas  a  prominence  which  they  did 
not  have  for  the  author  himself.  Connected  with 
this  latter  interpretation,  the  fallacy,  as  Creighton 


518  A  TEXT-BOOK  OF  LOGIC 

observes,  "appears  in  connected  arguments  of  any 
kind  in  which,  while  the  facts  are  not  actually  mis- 
stated, certain  aspects  of  them  are  so  disproportion- 
ately dwelt  upon  and  emphasised,  at  the  expense  of 
the  rest,  that  a  false  idea  of  the  subject  in  its  en- 
tirety is  the  result.  In  this  wider  form,  this  fallacy 
is  one  that  may  be  described  as  the  particular  vice 
of  special  pleading;  and  the  caution  that  may  be 
suggested  against  it  is,  in  the  language  of  the 
astronomer,  to  make  allowances  for  the  'personal 
equation'  both  in  one's  own  thinking  and  in  that  of 
others." 

Composition.  The  fallacy  of  composition,  like 
its  converse,  the  fallacy  of  division,  turns  on  the 
distinction  between  the  distributive  and  collective 
use  of  terms.  This  distinction,  it  will  be  remem- 
bered, is  based  on  the  fact  that  we  may  predicate 
qualities  and  relations  of  a  class  without  at  the 
same  time  predicating  those  qualities  or  relations 
of  the  individuals  that  constitute  the  class;  and, 
conversely,  we  may  predicate  qualities  and  relations 
of  the  individuals  that  constitute  a  class  without  at 
the  same  time  predicating  those  qualities  or  rela- 
tions of  the  class.  Now,  we  are  guilty  of  the  fal- 
lacy of  composition  when,  having  predicated  some- 
thing of  a'  term  used  distributively,  that  is,  of  each 
of  the  individuals  that  fall  under  the  term,  we  sup- 
pose that  the  predicate  belongs  to  the  term  in  its 
collective  sense,  that  is,  of  the  individuals  taken  as 
a  group.  "We  must  not  argue,"  to  use  Jevons'  illus- 


FALLACIES  519 

trations,  "that  because  every  member  of  a  jury  is 
very  likely  to  judge  erroneously,  the  jury  as  a  whole 
is  also  very  likely  to  judge  erroneously;  nor  that  be- 
cause each  of  the  witnesses  in  a  law  case  is  liable  to 
give  false  or  mistaken  evidence,  no  confidence  can 
be  reposed  in  the  concurrent  testimony  of  a  number 
of  witnesses.  It  is  by  a  fallacy  of  Composition  that 
protective  duties  are  still  sometimes  upheld.  Be- 
cause any  one  or  any  few  trades  which  enjoy  pro- 
tective duties  are  benefited  thereby,  it  is  supposed 
that  all  trades  at  once  might  be  benefited  similarly; 
but  this  is  impossible,  because  the  protection  of  one 
trade  by  raising  prices  injures  others." 

Division.  The  fallacy  of  division  is,  as  was  said, 
the  converse  of  the  fallacy  of  composition.  It  was 
so  considered  by  Aristotle.  It  occurs  when  we  sup- 
pose that  a  statement  that  is  true  of  a  group  is  true 
of  the  individuals  of  the  group.  If,  for  example, 
it  is  true  that  a  particular  class  of  college  students 
are  bright,  it  does  not  follow  that  this  is  true  of 
each  or  any  particular  one  of  the  members  of  the 
class,  any  more  than  it  follows  that  because  a  jury 
can  be  relied  on  to  reach  a  just  verdict  that  a  sim- 
ilar confidence  can  be  placed  in  any  one  of  the  jury- 
men. Gibson  has  called  attention  to  an  interesting 
illustration  of  this  fallacy  to  be  found  in  Thomas  a 
Kempis'  Imitatio  Christi.  In  the  paragraph  refer- 
red to,  the  writer  is  exhorting  the  'good  monk'  not 
to  seek  any  earthly  delight,  but  to  remain  alone  in 
his  cell.  The  argument  by  which  this  advice  is  sup- 
ported reads:  "What  canst  thou  see  elsewhere 


520  A  TEXT-BOOK   OF  LOGIC 

which  here  thou  seest  not?  Behold  the  sky  and  the 
earth,  and  all  the  elements,  for  of  these  are  all 
things  made."  Expressing  this  argument  syllogis- 
tically,  Gibson  detects  the  fallacy  of  division  in  the 
middle  term.  Thus: 

The  elementary  substances    (in  organised  combination) 

are  the  whole  material  world. 
The  objects  included  in  the  prospect  from  your  cell  are 

the  elementary  substances   (not  so  combined). 
Therefore,  the  objects  included  in  the  prospect  from  your 

cell  are  the  whole  material  world. 

As  this  ilustration  suggests,  the  fallacy  of  division, 
in  common  with  many  others,  is  most  liable  to  occur 
in  continuous  discourse,  and  the  value  of  putting 
the  subject-matter  of  such  discourse  into  the  logical 
forms  suitable  to  them  is  that  we  may  the  more 
easily  detect  any  fallacy  lurking  in  our  thought,  or 
in  the  forms  in  which  that  thought  is  expressed. 

Accident.  The  fallacy  of  accident  occurs  when 
we  suppose  that  what  is  true  of  a  term  used  in  a 
relatively  indeterminate  or  unconditioned  sense,  is 
true  of  the  term  when  used  in  a  relatively  deter- 
minate or  conditioned  sense.  The  Latin  name  of 
the  fallacy  is,  Argumentum  a  dicto  simpliciter  ad 
dictum  secundum  quid.  It  is,  that  is  to  say,  a  tran- 
sition from  what  is  true  of  an  indeterminate  state- 
ment to  what  is  true  of  the  same  statement  'with  a 
modification/  In  other  words,  it  consists  in  secur- 
ing assent  to  a  statement  in  a  general  form,  and 
then  proceeding  as  if  it  held  under  some  special 


FALLACIES  521 

circumstance.  If  we  supposed,  for  example,  that 
because  it  is  right  for  a  man  to  inculcate  his  own 
opinions,  it  is,  therefore,  right  for  a  magistrate  to 
use  his  position  to  enforce  his  own  political  views, 
we  should  be  guilty  of  this  fallacy.  For,  as  Mellone, 
from  whom  this  illustration  is  taken,  remarks,  "we 
cannot  infer  of  his  special  powers  as  a  magistrate 
what  is  only  true  of  his  general  rights  as  a  man." 
We  may  often  detect  the  fallacy  in  our  thoughts 
about  moral  questions.  Thus,  in  discussing  such 
questions,  "one  may  insist  that  all  men  by  nature 
seeks  after  the  good,  meaning  that  each  man  acts 
sub  specie  boni,  and  is  therefore  seeking  after  some 
kind  of  good,  even  when  he  is  pursuing  his  own 
pleasure.  But,  in  continuing  the  argument,  he  may 
use  the  term  'good'  in  a  differentiated  sense  —  e.  g., 
in  the  sense  of  the  common  good,  or  the  good  of 
humanity  —  and  come  thereby,  through  a  fallacy  of 
accident,  to  the  conclusion  that  all  men  by  nature 
seek  the  general  good." 

The  Converse  Fallacy  of  Accident  occurs  when 
we  suppose  that  what  is  true  of  a  term  used  in  a 
determinate  or  conditioned  sense  is  true  of  the  term 
when  used  in  an  indeterminate  or  unconditioned 
sense.  The  Latin  name  of  the  fallacy  is,  Argumen- 
tum  a  dicto  secundum  quid  ad  dictum  simpliciter. 
The  following  illustrations  will  be  sufficient  to  make 
the  nature  of  this  fallacy  obvious.  For  example, 
let  us  suppose  that  it  can  be  shown  that  the  syllo- 
gism is  of  no  use  in  the  discovery  of  new  truth,  are 
we  warranted  in  supposing,  as  the  early  modern 


522  A  TEXT-BOOK  OF  LOGIC 

critics  of  the  syllogism  seem  to  have  done,  that  it 
is,  therefore,  of  no  use  whatever  ?  Or,  if  philosophy 
'bakes  no  bread/  is  it,  therefore,  useless?  The 
affirmative  answer  to  both  these  questions  involves 
the  converse  fallacy  of  accident. 

Structural  Ambiguity.  In  the  chapter  on  the 
proposition,  it  was  pointed  out  that  particular 
statements  are  often  ambiguous,  not  because  the 
terms  in  which  they  are  expressed  are  ambiguous, 
but  because  the  structure  of  the  sentences  in  which 
ideas  are  expressed  are  so.  It  is  to  the  grammatical 
structure  of  sentences,  for  example,  that  we  must 
attribute,  in  part,  the  difficulty  sometimes  expe- 
rienced in  determining  the  subject  and  predicate 
terms  of  given  propositions.  Whenever  syntactical 
relations  obscure  the  meaning  of  sentences  or  para- 
graphs, there  is  presented  a  hindrance  to  the  correct 
interpretation  of  propositions.  Difficulties  of  the 
kind  in  question  are  more  possible  in  the  classical 
languages  where  the  word  order  in  sentences  is 
more  variable,  and  where  oblique  constructions  are 
more  common,  than  in  English;  but  something  of 
the  same  sort  is  seen  in  English  poetry  in  which  a 
departure  from  the  relative  simplicity  of  the  ordi- 
nary prose  sentence  is  often  made  necessary  by  the 
demands  of  metrical  composition. 

Amphibole.  Now,  whenever  the  structure  of  the 
sentences  in  which  ideas  are  expressed,  in  prose 
or  in  poetry,  leads  to  opposed  interpretations  of 
such  sentences,  we  have  the  typical  fallacy  of  amphi- 
bole.  Sometimes  sentences  whose  structure  renders 


FALLACIES  523 

their  interpretation  difficult,  although  not  neces- 
sarily ambiguous,  are  spoken  of  as  amphibolic. 
This  is  a  view  similar  to  that  sometimes  taken  of 
words,  when  any  degree  of  indefiniteness  is  thought 
sufficient  to  render  them  equivocal.  This  seems  to 
us  too  loose  an  interpretation  of  these  fallacies.  As 
we  have  pointed  out  in  regard  to  words,  there  is 
also  a  certain  freedom  in  the  use  of  syntactical 
relations  that  is  allowable  and  necessary  if  partic- 
ular shades  of  meaning  are  to  get  expressed  in  the 
sentences  we  employ.  The  object  that  the  transla- 
tion of  sentences  into  propositions  keeps  in  view 
is,  not  to  give  all  statements  an  equal  clearness,  but 
to  bring  out  the  exact  degree  of  clearness  that  be- 
longs to  each  of  our  statements.  A  certain  indefi- 
niteness of  meaning  may  be  characteristic  of  propo- 
sitions, therefore,  without  involving  them  in  the 
fallacy  of  amphibole.  Before  we  can  convict  any 
statement  of  being  amphibolic,  we  must  have  ex- 
hausted all  the  means  at  our  disposal  to  interpret 
the  statement,  and  to  give  it  an  expression  which 
truly  represents  its  meaning.  If  it  then  remains 
ambiguous,  if,  that  is,  our  attempt  to  give  the  state- 
ment a  prepositional  form  is  defeated  on  account  of 
its  equivocal  syntax,  we  may  properly  regard  it  as 
an  example  of  the  fallacy  of  amphibole.  An  illus- 
tration of  this  statement  may  be  found  in  the  often 
quoted  lines  of  Shakespeare,  The  Duke  yet  lives 
that  Henry  shall  depose.'  We  are  baffled  in  any 
attempt  to  put  this  sentence  into  the  form  of  a 
proposition,  because  its  structure  does  not  enable 


524  A  TEXT-BOOK  OF  LOGIC 

us  to  determine  whether  it  means,  The  Duke  yet 
lives  who  shall  depose  Henry/  or,  The  Duke  yet 
lives  who  shall  be  deposed  by  Henry/  Such  a 
statement,  therefore,  is  essentially  amphibolic.  The 
student  will  recall,  in  further  illustration,  many  of 
the  utterances  of  the  oracles,  for  instance,  'If 
Croesus  should  wage  war  against  the  Persians,  he 
would  destroy  a  mighty  empire/  As  further  ex- 
amples we  may  cite,  'It  is  possible  for  thee  the 
enemy  to  overcome/  The  lion  David  slew/ 

False  Parenthesis.  Closely  connected  with  the 
foregoing,  is  the  fallacy  of  false  parenthesis.  It 
consists  essentially  in  an  uncertainty  with  regard 
to  the  relations  of  the  main  and  subordinate  clauses 
of  a  sentence.  For  example,  'I  ruined  the  cause 
and  injured  my  own  prospects  which  I  deeply  re- 
gret/ a  statement  that  may  mean  either,  'I  ruined 
the  cause,  and  injured  my  own  prospects  which  I 
deeply  regret/  or,  'I  ruined  the  cause  and  injured 
my  own  prospects,  which  I  deeply  regret/  A  sim- 
ilar fallacious  statement  is  'I  will  begin  and  finish 
the  task  tomorrow/  The  advertising  columns  of 
our  newspapers  are  sometimes  said  to  provide  us 
with  humorous  illustrations  of  the  fallacy  of  paren- 
thesis. For  instance: 

LOST  —  A  valuable  silk  umbrella  belonging  to  a  gentle- 
man with  a  curiously  carved  head. 

WANTED  —  A  groom  to  look  after  two  horses  of  a  pious 
frame  of  mind. 

FOR  SALE  —  A  Newfoundland  dog ;  will  eat  anything, 
particularly  fond  of  children. 


FALLACIES  525 

We  introduce  these  instances,  not  in  order  to 
subscribe  to  the  view  that  they  are  amphibolic  in 
character,  but  to  point  out  that  if  these  are  to  be 
admitted  as  examples  of  amphiboly,  then  any  badly 
constructed  sentence  would  have  to  be  included 
whether  or  not  their  meaning  was  involved  in  am- 
biguity. This  is  a  view  to  which,  as  we  said  above, 
we  cannot  subscribe. 

Fallacies  of  Implication.  The  second  main  class 
of  fallacies  which  we  have  now  to  consider  com- 
prises those  that  occur  when  for  any  reasons  we 
mistake  the  implications  of  prepositional  state- 
ments. The  difficulties  that  confront  our  efforts  to 
give  to  any  statement  a  prepositional  form  have 
been  considered  already,  and  in  contrast  to  these, 
the  ones  with  which  we  are  now  concerned  presup- 
pose that  those  difficulties  have  been  overcome,  and 
that  we  know  unequivocally  the  significance  that 
particular  statements  have.  Until  we  are  sure  what 
the  asserted  meaning  of  a  proposition  is,  tre  cannot 
raise  the  question  whether,  and  if  so  what,  further 
or  implied  meaning  it  can  have. 

It  will  be  remembered  that  by  implication  is 
meant  the  unexpressed  signification  of  a  logical 
proposition,  and  that  implications  may  assume  one 
or  the  other  of  two  forms.  In  the  first  form,  the 
unexpressed  or  implied  propositions  may  be  related 
to  the  given  proposition  in  the  way  of  opposition, 
in  the  second  form,  they  may  be  related  to  the 
given  proposition  in  the  way  of  eduction.  These 


526  A  TEXT-BOOK  OF  LOGIC 

distinctions  will  provide  us  a  natural  and  easy 
method  of  classifying  the  fallacies  of  implication. 

Fallacies  of  Opposition  occur  when,  from  state- 
ments accepted  as  true  or  false,  other  statements 
dealing  with  the  same  subject-matter  are  derived, 
the  truth  or  falsity  of  which  is,  mistakenly,  sup- 
posed to  rest  upon  the  principles  that  determine  the 
relations  of  opposed  propositions.  It  has  been 
shown  above  that  there  are  four  kinds  of  relation 
between  propositions  in  opposition,  —  contrariety, 
subcontrariety,  subalternation,  and  contradiction. 
These  relations  have  been  studied,  and  the  propo- 
sitions between  which  each  obtains  have  been  indi- 
cated. '  In  view,  therefore,  of  what  we  have  learned 
with  respect  to  this  class  of  implication,  it  is  readily 
seen  that,  in  respect  to  this  class,  our  thought  be- 
comes fallacious  when  we  suppose  that  the  prin- 
ciples of  opposition  justify  a  statement  which,  as 
a  matter  of  logic,  they  are  incapable  of  support- 
ing. Or,  to  put  it  another  way,  any  statement 
which  avowedly  rests  upon  the  principles  of  opposi- 
tion is  fallacious  if  it  can  be  shown  that  those  prin- 
ciples fail  to  give  it  the  necessary  support. 

In  general,  it  is  quite  obvious  that  there  are  as 
many  fallacies  of  opposition  as  there  are  pairs  of 
propositions  between  which  relations  of  opposition 
may  hold.  Some  of  these  relations  are  in  themselves 
so  obvious,  the  relation  of  contradiction,  for  in- 
stance; and  others  lose  so  readily  whatever  obscur- 
ity they  may  have  when  they  occur  between  certain 
pairs  of  propositions,  that  it  is  not  necessary  to 


FALLACIES  527 

consider  all  the  possible  fallacies  of  opposition.  All, 
therefore,  that  we  shall  attempt  is  to  point  out 
some  of  the  difficulties  that  may  be  experienced  in 
the  effort  to  conform  our  thinking  to  the  principles 
of  opposition. 

And,  in  the  first  place,  we  may  consider  the 
fallacy  of  contrariety  which  occurs  when  we  sup- 
pose that  the  falsity  of  one  universal  proposition, 
A  or  E,  involves  the  truth  or  falsity  of  the  other, 
E  or  A.  It  may  be  false,  for  example,  that  'None 
of  the  members  of  the  team  are  bona  fide  students/ 
but  it  does  not ,  therefore,  follow  that  'All  the 
members  of  the  team  are  bona  fide  students,* 
and  it  does  not  follow  because,  it  might  still  be 
true  that  'Some  of  the  members  of  the  team  are  not 
bona  fide  students.'  It  is  certainly  very  easy  for 
the  untrained  mind  to  proceed  from  the  falsity  of  a 
universal  to  the  truth  of  its  logical  contrary,  and 
one  is  particularly  exposed  to  this  error  when  the 
latter  statement  is  separated  in  our  discourse  from 
the  former  by  an  appreciable  lapse  of  time.  But, 
as  we  saw  above,  the  statement  of  what  is  false  in 
a  universal  form  does  not  enable  us  to  say  anything 
with  respect  either  to  the  truth  or  falsity  of  its 
contrary.  In  such  cases  the  contrary  is  always  in- 
volved in  doubt. 

In  the  second  place,  we  are  exposed  to  a 
fallacy  of  sub  contrariety  when  we  attempt  to  argue 
from  the  truth  of  a  particular  proposition,  I  or 
O,  to  the  falsity  of  another  particular  proposition, 
0  or  I.  We  run  into  this  error  when  we  forget 


528  A  TEXT-BOOK   OF  LOGIC 

that  two  particular  propositions  dealing  with  the 
same  subject-matter,  one  of  which  is  affirmative 
and  the  other  negative,  may  both  be  true.  From  the 
statement,  for  example,  that  'Some  of  those  who 
have  given  their  word  are  keeping  it  faithfully/  it 
does  not  follow  that  'Some  of  those  who  have  given 
their  word  are  not  keeping  it  faithfully'  is  false, 
since  this  latter  statement  might  be  true  of  any  of 
those  not  included  in  the  original  statement. 

In  the  third  place,  fallacies  of  sub  alternation  may 
arise  when  we  argue  either  from  the  falsity  of  a 
universal  propostion,  or  from  the  truth  of  a  par- 
ticular proposition.  The  falsity  of  a  universal  propo- 
sition, 'All  that  I  have  done  for  you  has  gone  for 
nought/  might  very  well  seem  to  involve  the  falsity 
of  the  particular  subaltern,  'Some  of  the  things  I 
have  done  for  you  have  gone  for  nought;'  but  this 
would  not  necessarily  be  the  case,  because  the  truth 
or  falsity  of  the  subaltern  proposition  depends  in 
this  case  upon  the  degree  of  falsity  of  the  original 
proposition,  and  it  is  exactly  this  that  we  cannot  de- 
termine from  that  proposition  itself.  Unless  it  were 
so  common,  one  would  hardly  think  it  necessary  to 
call1  attention  to  the  other  fallacy  of  subalternation, 
the  fallacy,  namely,  that  is  involved  in  proceeding 
from  the  truth  of  a  particular  statement  to  the  truth 
of  its  corresponding  universal.  It  may,  for  example, 
be  quite  clear  that  from  the  statement  that  'Some 
books  are  dull/  we  cannot  proceed  to  the  statement 
that  'All  books  are  dull/  but  we  dare  say,  it  is  not 
equally  obvious  that  we  cannot  proceed  from  the 


FALLACIES  529 

statement,  'Some  planets  move  in  their  own  orbits', 
to,  'All  planets  move  in  their  own  orbits.'  The  rea- 
son why  we  cannot  argue  from  the  truth  of  a  part- 
ticular  statement  to  either  the  truth  or  falsity  of 
the  universal  of  the  same  quality  seems  to  be  that 
we  have  no  means  of  determining,  by  an  examina- 
tion of  the  original  statement,  the  precise' amount 
of  truth  that  is  claimed  by  it,  that  is,  whether  it 
states  the  whole  truth  about  its  subject,  or  only 
part  of  it. 

Fallacies  of  Eduction.  Eductions  were  defined 
above  as  those  relations  which  propositions  dealing 
with  the  same  subject-matter  have  to  one  another 
when  they  express  what  is  true  about  this  subject- 
matter  from  different  points  of  view.  There  are, 
as  we  said,  two  fundamental  methods  for  deter- 
mining these  relations,  obversion  and  conversion, 
and  it  is  with  respect  to  these  methods,  therefore, 
that  fallacies  are  likely  to  occur.  An  eductive  fal- 
lacy may,  consequently,  be  defined  as  an  error  of 
•implication  due  to  a  misunderstanding  of  obversion, 
of  conversion,  or  of  both. 

The  fallacy  of  obversion  is  most  likely  to  occur 
when  for  the  contradictory  of  the  predicate  of  an 
original  proposition  we  substitute  its  contrary  in 
the  obverse  proposition.  Now  by  contrary  terms 
we  mean  those  which,  although  opposed  to  one  an- 
other, do  not  exhaust  between  them  the  particular 
universe  of  discourse  to  which  they  both  belong. 
Black  and  white  are,  in  this  sense,  contrary,  but 
they  are  not  contradictory,  terms.  By  a  contra- 

34 


530  A  TEXT-BOOK  OF  LOGIC 

dictory  term  we  mean  one  that,  together  with  the 
original  term,  does  exhaust  the  universe  of  discourse 
to  which  both  terms  belong.  Thus,  black  and  not- 
black  are  contradictory,  but  they  are  not  contrary, 
terms.  It  is,  then,  a  confusion  of  contrary  with 
contradictory  terms,  in  the  sense  in  which  these 
have  been  defined,  that  gives  rise  to  the  fallacy  of 
obversion.  Thus,  it  would  be  quite  fallacious,  for 
the  reason  already  assigned,  if  we  supposed  that 
we  were  warranted  in  saying  of  a  particular  indi- 
vidual that  he  was  bad,  if  all  we  knew  was  that  he 
is  not  good;  good  and  bad  are  contrary,  they  are 
not  contradictory,  terms.  Again,  if  we  supposed 
that  the  obverse  of  the  proposition  'He  is  not  happy, 
was  'He  is  unhappy/  there  would  be  as  complete 
misunderstanding  of  what  was  implied  in  the  first 
statement  as  if  we  supposed  that  because  a  certain 
object  was  not  red  that  it  was,  therefore,  green. 

Fallacies  of  Conversion  are  most  likely  to  occur 
in  the  case  of  the  universal  affirmative,  and  the 
particular  negative  propositions.  In  the  latter  case, 
the  fallacy  occurs  when  we  suppose  that  from  a 
particular  negative  proposition  anything  can  be 
asserted  merely  by  converting  it.  It  is  quite  true, 
for  example,  that  'Some  elements  are  not  liquid/ 
and  also  that  'Some  liquids  are  not  elements/  but 
the  one  statement  does  not  follow  from  the  other 
by  simple  conversion.  Again,  a  fallacy  of  conver- 
sion occurs  when  we  suppose  that  the  universal 
affirmative  proposition  can  be  simply  converted,  a 
supposition  that  is  based  on  the  false  assumption 


FALLACIES  531 

that  both  terms  of  the  proposition  are  distributed. 
In  universal  affirmative  propositions,  as  we  have 
seen,  the  predicate  terms  are  undistributed;  and, 
consequently,  when,  through  conversion,  these  terms 
become  the  subjects  of  new  propositions,  these  prop- 
ositions must  be  particular  in  quantity.  The  neg- 
lect of  this  consideration  leads  directly  to  a  fallacy 
of  conversion. 

Fallacies  of  Inference.  The  class  of  fallacies  to 
which  we  now  direct  attention  includes  the  errors 
to  which  our  thinking  is  exposed  when  it  is  con- 
fronted by  the  difficulties  that  are  involved  in  the 
more  complex  logical  processes  known  as  argu- 
ments. The  two  classes  of  fallacy  already  con- 
sidered, the  fallacies  of  interpretation  and  implica- 
tion, are  concerned  with  the  errors  to  which  thought 
is  liable  when  it  deals  with  single  statements;  but 
it  is  not  until  these  simpler  errors  have  been  avoided, 
not  until  single  statements  have  been  given  a  strictly 
logical  form  and  content,  that  there  comes  into  view 
the  class  of  fallacy  that  is  connected  with  our  at- 
tempt to  put  into  their  logical  relations  such  logically 
determined  propositions.  For,  in  an  argument,  not 
only  must  the  constituent  propositions  be  free  from 
ambiguity,  but  the  relations  between  these  proposi- 
tions must  be  precisely  determined.  It  is  perfectly 
obvious,  therefore,  that  the  avoidance  of  the  fal- 
lacies of  interpretation  and  implication  is  essential, 
if  we  are  to  meet  and  overcome  the  difficulties  that 
are  occasioned  by  the  more  complex  character  of 
our  thinking  in  the  process  of  argument.  We  may, 


532  A  TEXT-BOOK  OF  LOGIC 

therefore,  say  that  just  as  the  avoidance  of  the  fal- 
lacies of  interpretation  are  presupposed  by  any 
attempt  to  avoid  the  fallacies  of  implication,  so  the 
avoidance  of  both  these  classes  of  fallacy  is  presup- 
posed by  any  attempt  to  overcome  the  fallacies  of 
inference. 

Arguments,  from  the  time  of  Aristotle,  have 
been  recognised  to  be  of  two  kinds:  those,  namely, 
that  start  with  the  recognition  of  some  general 
principle,  and  those  that  start  with  the  collection 
of  a  number  of  particular  facts.  In  the  former,  the 
aim  is  to  bring,  through  the  mediation  of  a  middle 
term,  some  particular  fact  under  the  principle  which 
constitutes  what  is  called  the  major  premise  of  the 
argument;  in  the  latter,  it  is,  through  an  analysis 
of  particular  facts,  to  state  a  principle  that  shall 
exhibit  what  is  common  to  all  the  facts  examined, 
and,  if  possible,  to  extend  that  principle  to  other 
facts  which  either  have  not  been  examined,  or  which 
are  not  known  to  exist.  It  is  usual  to  call  the 
former  kind  of  argument  deductive,  and  the  latter, 
inductive;  and,  although  there  is  a  danger  of  sup- 
posing, falsely,  that  they  constitute  quite  separate 
logical  processes,  we  may  use  these  names,  deductive 
and  inductive,  for  the  purpose  of  classifying  the 
fallacies  of  inference.  The  deductive  fallacies  will 
include  those  errors  that  arise  in  connection  with 
the  syllogism,  and  the  inductive  fallacies  will  include 
those  that  arise  in  connection  with  the  various  steps 
through  which  it  is  necessary  to  pass  in  our  efforts 
to  establish  causal  connections. 


FALLACIES  533 

/ 

The  Deductive  Fallacies.  Whenever  an  argument 
starts  from  the  conscious  acceptance  of  a  general 
truth  about  its  subject-matter,  and  proceeds  to  show 
that  some  particular  fact  is  a  special  instance  of  that 
truth,  it  is  said  to  be  a  deductive  argument.  Now, 
since  we  accept  such  general  truths  as  are  the 
starting  points  of  deductive  arguments  in  either 
one  or  the  other  of  three  forms,  in  the  forms, 
namely,  of  categorical,  hypothetical,  or  disjunctive 
propositions,  these  arguments,  as  we  have  seen, 
assume  a  form  and  character  which  corresponds  to 
the  difference  in  the  method  and  principle  by  which 
thought,  in  each  case,  proceeds  to  its  conclusion. 
In  consequence  of  this  fact,  we  found  it  necessary 
to  consider  categorical  arguments,  hypothetical 
arguments,  and  disjunctive  arguments  separately, 
and  to  give  special  attention  to  the  rules  by  which 
thought,  in  each  type  of  argument,  is  controlled. 
It  follows,  from  this  statement  with  respect  to  the 
various  forms  of  deductive  arguments,  that  the 
deductive  fallacies  can  be  classified  most  conve- 
niently by  following  the  line  of  cleavage  between 
the  arguments  in  connection  with  which  they  are 
likely  to  occur.  In  the  following  sections,  therefore, 
we  shall  pass  in  review  what  we  may  call  the  cate- 
gorical, hypothetical,  and  disjunctive  fallacies,  the 
fallacies  which  occur,  or  are  liable  to  occur,  in  those 
types  of  argument  to  which  similar  descriptive 
names  have  been  given. 

Categorical  Fallacies  may  be  defined  as  those  mis- 
takes in  reasoning  which  render  the  conclusions  of 


534  A  TEXT-BOOK  OF  LOGIC 

categorical  arguments  erroneous.  These  fallacies 
fall  conveniently  into  two  groups,  according  as  the 
error  lies  in  the  terms,  or  in  the  character  of  the 
proposition  of  the  syllogism.  To  the  former  group 
we  may  assign  the  fallacies  of  four  terms,  and  to 
the  latter,  the  fallacies  of  insufficient  premises. 

Fallacies  of  Four  Terms  occur  as  a  breach  of 
the  rule  which  states  that  a  syllogism  must  contain 
three,  and  only  three,  terms.  Their  occurrence  is 
due  to  a  failure  to  rid  the  terms  of  a  syllogism  of 
ambiguity.  Now,  since  ambiguity  may  occur  either 
in  the  connotation  or  in  the  denotation  of  a  term, 
and  may  attach  to  any  one  of  the  terms  of  a  syllo- 
gism, it  is  evident  that  the  fallacies  of  four  terms 
are  of  two  kinds ;  those,  namely,  which  occur  when 
the  meaning  of  any  of  the  terms  of  a  syllogism  is 
ambiguous,  and  those  which  are  due  to  a  mistaken 
distribution  of  any  of  the  terms  of  a  syllogism. 
Among  the  former,  it  is  usual  to  call  special  atten- 
tion to  the  case  of  the  middle  term,  but  it  should 
be  remembered  that  the  ambiguity  of  the  major  or 
of  the  minor  term  may  also  invalidate  an  argu- 
ment by  giving  rise  to  the  fallacy  of  four  terms. 
When  the  fallacy  of  four  terms  invalidates  a  syllo- 
gism on  account  of  the  connotative  ambiguity  of  the 
middle  term,  it  takes  the  special  name  of  ambiguous 
middle;  when  an  argument  is  invalid  on  account  of 
a  similar  ambiguity  of  the  major  term,  the  fallacy  is 
called  ambiguous  major;  and  when  ambiguity  in  the 
meaning  of  the  minor  term  destroys  the  validity  of 
an  argument,  the  fallacy  is  called  ambiguous  minor. 


FALLACIES  535 

It  is  not  necessary  to  give  illustrations  of  all  these 
fallacies.  The  following  will  serve  to  show  the  form 
in  which  they  are  likely  to  occur.  If,  as  Jevons 
remarks,  we  argue  "that  'all  metals  are  elements  and 
brass  is  a  metal,  therefore  it  is  an  element/  we 
should  be  using  the  middle  term  'metal'  in  two  dif- 
ferent senses,  in  one  of  which  it  means  the  pure  sim- 
ple substances  known  to  chemists  as  metals,  and  in 
the  other  a  mixture  of  metals  commonly  called  metal 
in  the  arts,  but  known  to  chemists  by  the  name 
alloy."  Or,  if  we  argued  "that  'what  is  right  should 
be  enforced  by  law,  and  that  charity  is  right  and 
should  be  enforced  by  law'  .  .  .  it  is  evident  that 
'right'  is  applied  in  one  case  to  what  the  conscience 
approves,  and  in  another  use  to  what  public  opinion 
holds  to  be  necessary  for  the  good  of  society." 

The  other  type  of  fallacy  which  results  in  break- 
ing an  argument  under  the  weight  of  four  terms, 
is  due  to  a  disregard  of  the  denotation  or  distribu- 
tion of  the  terms  of  a  syllogism.  In  these  cases,  the 
erroneous  conclusion  results  from  a  neglect  of  the 
extent  of  a  term's  meaning,  rather  than  to  a  dis- 
regard of  the  meaning  itself.  In  other  words,  it  is 
a  fallacy  of  the  division,  not  a  fallacy  of  the  defi- 
nition, of  a  term.  Now,  as  we  have  seen,  the  dis- 
tribution of  the  terms  of  a  syllogism  is  subject 
to  special  rules.  In  respect  of  the  middle  term,  the 
rule  states  that  this  term  must  be  distributed  in  one, 
at  least,  of  the  premises ;  and  in  respect  of  the  major 
and  minor  terms,  the  rule  states  that  if  either  of 
these  terms  is  distributed  in  the  conclusion,  it  must 


536  A  TEXT-BOOK  OF  LOGIC 

have  been  distributed  in  the  corresponding  premise. 
When  the  rule  relating  to  the  middle  term  is  dis- 
regarded, the  resulting  fallacy  is  known  as  undis- 
tributed middle;  and  when  the  rule  relating  to  the 
terms  of  the  conclusion  is  disregarded,  the  resulting 
fallacy,  in  the  case  of  the  major  term,  is  known  as 
illicit  process  of  the  major,  and,  in  the  case  of  the 
minor,  as  illicit  process  of  the  minor.  The  fol- 
lowing illustrations  will  throw  light  on  these  state- 
ments. If  we  should  argue,  for  example,  that  be- 
cause "all  rash  men  are  confident,  and  all  brave  men 
are  confident,"  therefore,  "all  rash  men  are  brave," 
we  should  be  guilty  of  the  fallacy  of  undistributed 
middle.  Again,  if  we  argued  "that  'because  many 
nations  are  capable  of  self-gvoernment,  and  and 
that  nations  capable  of  self-government  should  not 
receive  laws  from  a  despotic  government,  therefore 
no  nation  should  receive  laws  from  a  despotic  gov- 
ernment/ we  should  be  clearly  exceeding  the  con- 
tents of  our  premises.  The  minor  term,  many 
nations,  was  undistributed  in  the  minor  premise," 
and  must  not,  consequently,  be  used  in  a  distributed 
sense  in  the  conclusion.  While  it  is  comparatively 
easy  to  detect  an  illicit  process  of  the  minor,  it  is 
much  more  difficult  as  a  rule  to  detect  an  illicit 
process  of  the  major.  The  following  from  Creighton 
is  an  example  of  the  latter  fallacy.  "All  rational 
beings  are  responsible  for  their  actions ;  brutes  are 
not  rational  beings;  therefore,  brutes  are  not  re- 
sponsible for  their  actions." 


FALLACIES  537 

Fallacies  of  Insufficient  Premises.  These  consti- 
tute the  second  class  of  categorical  fallacies,  and 
they  may  be  described  as  breaches  of  those  rules  of 
the  syllogism  that  were  considered  and  illustrated 
above  as  rules  of  quality  and  rules  of  quantity.  The 
rules  of  quality  refer  to  the  grounds  on  which  affir- 
mative and  negative  conclusions  can  be  based,  and 
the  rules  of  quantity  to  the  grounds  on  which  uni- 
versal and  particular  conclusions  can  be  based.  In 
the  main,  we  apprehend  that  these  rules  have  caused 
the  student  no  great  difficulty,  and  that  he  will  have 
become  familiar  with  their  application.  But  because 
limiting  instances  are  liable  to  cause  more  or  less 
confusion,  because,  that  is,  we  find  it  difficult  to  keep 
strictly  within  the  boundaries  within  which  any  set 
of  rules  applies,  we  direct  attention  again  to  the  fact 
that  there  are  conditions  which  preclude  certain 
prepositional  statements  from  rendering  valid  con- 
clusions. It  is  a  general  fact  that  conclusions  do 
not  follow  from  any  combination  of  propositions. 
If  we  wish  to  support  a  conclusion  by  premises  or 
grounds,  those  premises  must  have  a  character  from 
which  the  conclusion  can  be  shown  to  follow,  and 
that  means  that  a  certain  other  character  is  strictly 
forbidden.  Now,  if  this  is  true  of  particular  con- 
clusions, we  may  go  further  and  ask  whether  there 
are  any  combinations  of  propositions  which  support 
no  conclusion  whatever,  that  is,  whether  there  are 
any  limits  of  strictly  categorical  argumentation. 
Now  such  limits  to  all  categorical  inference  we  find 
in  the  two  cases  that  are  included  here  for  con- 


538  A  TEXT-BOOK  OF  LOGIC 

\ 

sideration,  the  cases,  namely,  of  negative  and  par- 
ticular premises.  We  have  shown  above  that  any 
attempted  reasoning  on  the  grounds  of  particular  or 
negative  premises  involves  us  in  one  or  other  of  the 
fallacies  of  distribution;  but  what  is  more  impor- 
tant to  remark  now  is  that  the  study  of  these  two 
cases  enables  us  to  insist  upon  certain  character- 
istics of  syllogistic  reasoning  which  are  fundamental 
to  our  understanding  and  employment  of  this  type 
of  argument.  The  syllogism,  it  should  be  observed, 
rests  upon  the  possibility  of  making  with  respect 
to  the  subject-matter  of  the  argument  an  affirmative 
and  universal  statement.  The  universal  statement 
need  not  be  affirmative,  and  the  affirmative  state- 
ment need  not  be  universal ;  but  unless  the  premises 
contain  the  statement  of  universal  affirmative  rela- 
tions, no  conclusion  whatever  can  be  drawn.  Con- 
versely, if  we  wish  to  ground  a  belief  on  premises 
from  which  it  can  be  shown  to  follow,  these  prem- 
ises, considered  as  a  combination  of  propositions, 
must  be  universal  and  affirmative.  Indeed,  this  is 
only  to  say  that  any  categorical  argument  must  con- 
form to  the  character  of  syllogistic  reasoning.  For, 
to  speak  of  syllogistic  reasoning  at  all,  is  to  imply 
that  conclusions  are  inferred  from,  or  rest  upon, 
statements  about  a  given  subject-matter  which  are 
affirmative  and  universal  in  the  sense  in  which  those 
terms  have  been  explained.  Now,  if  this  is  the  true 
character  of  the  syllogism,  it  follows  that  particular 
premises,  whether  they  be  both  negative,  or  both 
affirmative,  or  one  negative  and  the  other  affirm- 


FALLACIES  539 

ative,  cannot  express  the  structure  of  a  syllogistic 
argument,  because  they  do  not  contain  the  note  of 
universality;  and  that  negative  premises  also  fail 
to  do  so,  whether  both  premises  are  universal  or 
only  one  is,  since  they  fail  to  express  the  note  of 
affirmation.  To  ground  a  conclusion  upon  premises 
which  fulfil  only  one  of  the  conditions  of  a  cate- 
gorical -argument,  that  is,  upon  propositions  which 
are  affirmative  without  being  universal,  or  upon 
propositions  which,  although  universal,  are  not 
affirmative,  is  to  fall  into  one  or  the  other  of  the 
fallacies  of  insufficient  premises.  In  the  former 
case,  we  have  the  fallacy  of  particular  premises, 
and  in  the  latter,  the  fallacy  of  negative  premises. 

Hypothetical  Fallacies  may  be  defined  as  those 
mistakes  in  reasoning  which  render  the  conclusions 
of  hypothetical  arguments  erroneous.  Hypothetical 
arguments,  as  we  have  seen,  derive  their  character 
from  the  relation  of  antecedence  and  consequence 
which  is  expressed  in  their  major  premise.  Two 
observations  only  need  to  be  made  to  remind  our- 
selves of  the  nature  and  limits  of  hypothetical 
arguments.  The  first  is  that  the  major  premises  of 
such  arguments  are  always  hypothetical  proposi- 
tions, that  is,  propositions  which  state  a  relation 
between  two  possibilities.  From  the  fact  that  a 
relation  of  antecedence  and  consequence  is  always 
affirmed  between  these  two  possibilities  in  hypothet- 
ical propositions,  it  follows  that  the  acceptance  of  a 
hypothetical  statement  commits  us  to  the  belief  that 
the  possibility  which  is  expressed  as  the  consequent 


540  A  TEXT-BOOK  OF  LOGIC 

can  be  regarded  as  an  actual  fact,  only  when  the 
possibility  expressed  as  the  antecedent  states  a  con- 
dition which  is  known  to  be  fulfilled.  We  cannot 
argue  in  the  reverse  order,  that  is,  from  the  known 
existence  of  the  consequent  to  the  existence  of  the 
antecedent.  The  second  remark  is  that  the  major 
premise  affords  no  guarantee  that  the  condition  it 
states  is  anywhere  fulfilled,  and,  consequently,  no 
guarantee  that  the  fact  stated  in  the  consequent  is 
any  where  to  be  met  with.  Whether  the  antecedent 
or  consequent  is  a  fact  that  the  minor  premise  can 
affirm  or  deny,  depends  upon  whether  either  has 
been  observed.  Thus,  the  possibility  of  a  hypothet- 
ical argument  rests  upon  our  ability  to  affirm  or 
deny,  for  some  other  reason  than  the  major  premise 
itself  affords,  one  or  other  of  the  possibilities  be- 
tween which  the  major  premise  postulates  a  rela- 
tion; but  within  these  limits  the  validity  of  such 
arguments  depends  upon  a  proper  interpretation  of 
the  relation  between  antecedent  and  consequent  as- 
serted by  the  major  premise.  It  is,  consequently,  to 
a  misunderstanding  of  this  relation  that  we  must 
look  for  the  source  of  the  fallacies  which  render  the 
conclusions  of  hypothetical  arguments  erroneous. 

The  hypothetical  fallacies  are  due,  as  we  said 
just  now,  to  a  wrong  interpretation  of  the  relation 
between  antecedent  and  consequent  asserted  in  a 
hypothetical  proposition.  Now,  since  there  are  two 
terms  in  a  hypothetical  proposition  each  of  which 
we  may  affirm  or  deny,  the  relation  between  ante- 
cedent and  consequent  may  be  interpreted,  theo- 


FALLACIES  541 

retically,  in  any  one  of  four  possible  ways.  It  might 
be  interpreted  to  mean  that  (1)  if  the  antecedent 
is  affirmed,  the  consequent  may  also  be  affirmed; 
(2)  if  the  antecedent  is  denied,  the  consequent  may 
also  be  denied;  (3)  if  the  consequent  is  affirmed, 
the  antecedent  may  also  be  affirmed;  (4)  if  the  con- 
sequent is  denied,  the  antecedent  may  also  be  denied 
Now,  as  we  pointed  out  before,  it  is  only  when  the 
minor  premise  either  affirms  the  antecedent  or 
denies  the  consequent  that  the  relation  asserted  in 
the  major  premise  is  interpreted  correctly;  only 
two,  therefore,  of  the  alternatives  enumerated  above 
represent  truly  the  relations  involved  in  a  hypo- 
thetical proposition.  When  either  of  the  other  rela- 
tions is  asserted  in  the  minor  premise  of  an  argu- 
ment, that  is,  when  the  minor  either  affirms  the  con- 
sequent or  denies  the  antecedent,  ;the  argument 
must  be  rejected  as  fallacious.  The  fallacy  of  deny- 
ing the  antecedent  leads  to  an  eroneous  denial  of 
the  consequent,  and  the  fallacy  of  affirming  the  con- 
sequent leads  to  an  erroneous  affirmation  of  the 
antecedent.  Both  fallacies,  as  we  shall  see,  arise 
from  the  neglect  of  an  underlying  material  fact  of 
considerable  importance  for  a  correct  understanding 
of  the  hypothetical  syllogism. 

In  general,  it  may  be  remarked  that  the  hypo- 
thetical fallacies  are  due,  on  the  material  side,  to  a 
failure  to  recognize  the  complexity  and  interconnec- 
tion of  natural  events.  It  is  true  that  the  object 
of  our  study  of  nature  is  to  determine,  in  the  strict 
sense,  causal  connections,  that  is,  relations  between 


542  A  TEXT-BOOK  OF  LOGIC 

phenomena  of  such  a  nature  that,  not  only  does  the 
consequent  follow  from  the  antecedent,  but  the 
stated  antecedent  is  implied  in  the  occurrence  of 
the  consequent.  Our  knowledge  of  natural  events, 
however,  frequently  falls  below  this  standard,  and 
we  have  to  be  satisfied  with  the  affirmation  of  a  one- 
sided relation,  that  is,  with  the  statement  of  a  rela- 
tion between  antecedent  and  consequent  of  such  a 
nature  that  while  the  former  is  always  followed  by 
the  latter,  it  does  not  always  and  necessarily  pre- 
cede the  latter.  There  are  large  areas  of  knowl- 
edge, in  other  words,  in  which  the  relations  involved 
fail  to  display  the  characteristics  of  causal  con- 
nections, and  in  reference  to  them  we  are  bound 
to  recognise  what  Mill  called  a  plurality  of  causes. 
Now  it  seems  to  be  the  neglect  of  this  consideration 
that  is  really  at  the  foundation  of  the  fallacies 
which  befall  hypothetical  arguments.  For,  as  Mel- 
lone  states,  "if  we  deny  the  antecedent,  we  cannot, 
therefore,  deny  the  consequent,  for  the  latter  may 
be  true  for  other  reasons,  and  if  we  affirm  the  con- 
sequent, we  cannot  affirm  the  antecedent,  for  the 
consequent  may  result  from  other  reasons."  In 
either  case,  that  is  to  say,  we  must  recognise  the 
possible  existence  of  more  connections  between 
antecedent  and  consequent  than  the  one  which  is 
made  the  subject  of  statement  by  the  major 
premise,  and  this  possibility  places  limitations 
upon  the  interpretation  which  we  can  give  to 
hypothetical  statements.  It  is  true  that,  if  the  major 
premise  states  a  causal  connection  between  the 


FALLACIES  543 

antecedent  and  consequent,  we  may  argue  from 
the  affirmation  or  denial  of  the  former  to  the  affir- 
mation or  denial  of  the  latter,  and  vice  versa.  In 
any  other  case,  the  possible  operation  of  a  plurality 
of  causes  must  be  allowed  to  determine  the  limits 
which  we  place  upon  hypothetical  arguments.  From 
this  point  of  view,  it  seems  quite  clear  that  when 
we  argue,  "If  a  man's  character  is  avaracious,  he 
will  refuse  to  give  money  for  useful  purposes;  this 
man  refuses  to  give  money  for  useful  purposes, 
therefore,  this  man's  character  is  avaracious,"  the 
conclusion  is  erroneous,  not  merely  because  the 
minor  premise  affirms  the  consequent,  but  because, 
as  we  all  know,  there  are  other  reasons,  not  at  all 
connected  with  a  man's  character,  which  may  make 
a  refusal  of  the  kind  in  question  the  necessary  and 
right  course  for  him  to  pursue,  And  it  seems 
equally  obvious  that  when  we  argue,  'If  some  agree- 
ment is  not  speedily  arrived  at  between  employers 
and  workmen,  the  trade  of  the  country  will  be 
ruined,  an  agreement  will  not  be  arrived  at  and 
therefore  the  trade  of  the  country  will  be  ruined/ 
the  conclusion  is  erroneous,  not  merely  because  the 
antecedent  is  denied,  but  because  the  prosperity  of 
a  country  depends  upon  other  conditions  than  the 
one  specified  in  the  antecedent  of  the  major  premise. 
In  both  these  instances  we  see  that  the  breach  of  the 
formal  rule  of  hypothetical  arguments  is  tanta- 
mount, on  the  material  side,  to  the  neglect  of  the 
plurality  of  causes,  that  is,  to  the  failure  to  recog- 


544  A  TEXT-BOOK   OF  LOGIC 

nise  the  complexity  and  interconnection  of  natural 
events. 

Disjunctive  Fallacies  may  be  defined  as  those  mis- 
takes in  reasoning  which  render  the  conclusions  of 
disjunctive  arguments  erroneous.  Disjunctive  argu- 
ments, as  we  have  seen,  derive  their  character  from 
the  fact  that  the  major  premises  of  such  arguments 
state  a  series  of  alternative  predicates  any  one  or 
more  of  which,  as  a  matter  of  fact,  may  be  found 
to  qualify  their  subjects.  Any  conclusion  which  is 
reached  on  the  basis  of  a  disjunctive  major  premise 
is  valid  or  erroneous  according  as  the  enumerated 
alternatives  do  or  do  not  conform  to  the  conditions 
of  disjunctive  statements,  and  as  the  inference  is 
or  is  not  warranted  by  the  premises  on  which  it  is 
made  to  rest.  With  respect  to  the  nature  of  dis- 
junctive statements,  it  is  sufficient  to  recall  that 
these  must  satisfy  three  conditions.  First,  the 
alternatives  must  all  fall  within  a  single  universe; 
not  any  set  of  terms  that  we  can  state  in  the  form 
of  'either  —  or'  are,  in  the  logical  sense,  disjunctive. 
Second,  the  terms  of  the  disjunction  must  be  ex- 
haustive; all  the  species  that  fall  within  the  uni- 
verse must  be  enumerated  disjunctively.  Third,  we 
saw  that  the  alternatives  do  not  necessarily,  although 
they  sometimes  do,  exclude  each  other;  it  does  not 
follow,  therefore,  that  only  one  of  the  predicates 
can  belong  to  the  subject  under  the  conditions  that 
determine  a  particular  argument.  Whenever  we 
fail  to  observe  either  one  of  these  requirements  of 
disjunctive  statements  in  the  process  of  argument, 


FALLACIES  545 

we  are  guilty  of  one  or  another  of  the  disjunctive 
fallacies. 

The  fallacy  of  false  disjunction  occurs  when  we 
proceed  to  a  conclusion  on  the  ground  of  a  major 
premise  in  which  the  presented  alternatives  do  not 
all  belong  to  a  single  genus.  The  neglect  of  the  first 
positive  condition  of  disjunctive  statements  leads 
necessarily  to  fallacious  arguments,  because,  where 
it  is  not  satisfied,  there  is  no  common  field  within 
which  the  systematic  connections  of  things,  as  set 
forth  in  disjunctive  statements,  may  be  said  to  fall. 
A  failure  to  keep  clearly  before  oneself  the  fact 
that  disjunctive  alternatives  are  definitely  alter- 
natives within  a  single  field  of  knowledge,  reveals 
an  .entire  misapprehension  of  the  nature  of  disjunc- 
tive statements,  and  leads  unavoidably,  therefore, 
to  erroneous  conclusions.  When,  for  example,  we 
are  prepared  to  find  in  a  stranger  to  whom  we  have 
been  introduced  all  sorts  of  social  virtues  merely  on 
the  ground  that  he  has  come  from  our  home  town, 
or  when  race  prejudices  make  us  blind  to  the  vir- 
tues that  individuals  of  a  particular  race  display, 
we  are,  in  all  probability,  guilty  of  the  fallacy  of 
false  disjunction.  The  logical  process  underlying 
social  attitudes  of  the  kind  in  question  may  be  illus- 
trated as  follows :  'Either  from  my  home  town  or 
devoid  of  all  or  certain  current  social  virtues ;  from 
my  home  town,  therefore  not  devoid,  etc/ 

The  fallacy  of  incomplete  disjunction  occurs  when 
we  proceed  to  a  conclusion  on  the  ground  of  a  major 

35 


546  A  TEXT-BOOK  OF  LOGIC 

premise  in  which  the  presented  alternatives  are 
not  exhaustively  enumerated.  It  is  true,  of  course, 
that  the  observation  of  single  facts  may  lead  to  a 
disjunctive  statement  which  does  not  meet  the  con- 
dition of  complete  enumeration.  We  may  say,  for 
example,  This  tree  is  an  oak  or  an  ash/  But  prop- 
ositions of  the  kind  just  illustrated,  while  they  may 
serve  as  minor  premises  of  disjunctive  arguments, 
cannot  serve  as  major  premises,  for  the  reason  that, 
although  the  universe  within  which  the  alternatives 
fall  has  been  accurately  determined,  the  alternatives 
within  that  universe  have  not  been  completely  enu- 
merated. The  necessity  of  a  complete  enumeration 
of  the  alternatives  is  due  to  the  fact  that  the  dis- 
junctive syllogism  is  intended  to  show,  not  only 
what  a  thing  is,  but  also  to  determine,  within  the 
genus  to  which  it  belongs,  what  it  is  not.  Let  us 
suppose  that  a  particular  tree  is  either  an  oak  or  an 
ash.  Then,  if  we  argue,  This  tree  is  an  oak  or  an 
ash,  it  is  an  oak,  and  therefore  it  is  not  an  ash/  the 
argument  would  be  formally  valid,  and  the  conclu- 
sion would  be  true ;  but  if  we  supposed  that  the  con- 
clusion stated  the  whole  truth  about  the  subject,  we 
should  fall  into  error  due  to  the  incomplete  disjunc- 
tion of  the  major  premise.  Or,  to  take  another  illus- 
tration, let  us  suppose  that  a  particular  ore  is  not 
either  gold  or  copper.  If,  then,  we  were  to  argue, 
This  specimen  of  ore  is  either  gold  or  silver  or 
copper  or  antimony ;  it  is  not  either  gold  or  copper, 
and  therefore  it  is  either  silver  or  antimony/  we 
have  fallen  clearly  into  a  conclusion  which  is  not  at 


FALLACIES  547 

all  necessarily  true,  for  the  specimen  in  question 
might  be  none  of  those  enumerated  in  the  major 
premise.  Such  a  conclusion  is  erroneous  because  all 
the  species  of  the  genus  to  which  the  particular 
specimen  belongs  were  not  enumerated.  But,  some 
one  may  say,  we  cannot  always  meet  this  require- 
ment of  complete  enumeration,  and  are  we,  there- 
fore, precluded  from  arguing  validly  to  a  disjunctive 
conclusion  ?  The  answer  is  that  we  must  express  the 
indeterminate  state  of  our  knowledge  about  objects 
in  a  complete  enumeration  if  we  are  to  reach  valid 
conclusions,  and  we  may  do  this  without  necessarily 
possessing  an  exhaustive  knowledge  of  the  subject 
to  which  the  argument  refers.  Thus,  to  state  the 
above  argument  in  a  form  from  which  a  valid  con- 
clusion may  be  drawn  we  may  say,  This  specimen 
of  ore  is  either  gold  or  silver  or  copper  or  antimony 
or  some  other  species/  a  statement  which  does  not 
claim  complete  knowledge  of  the  subject-matter  of 
the  argument,  but  does  rest  upon  a  complete  deter- 
mination of  the  knowledge  that  is  possessed  about  it. 
The  fallacy  of  ambiguous  disjunction  occurs  when 
we  proceed  to  a  conclusion  on  the  ground  of  a  major 
premise  in  which  the  presented  alternatives  are  not 
precisely  determined  with  respect  to  their  exclusion. 
We  have  seen  that  any  proposition  of  the  form  *S  is 
either  A  or  B'  strictly  interpreted  means  *S  is  either 
A  or  else  B,'  but  we  also  saw  that  the  alternatives 
do  not  necessarily  preclude  the  possibility  that  *S 
may  be  both  A  and  B.'  Unless,  therefore,  we  take 
special  pains  to  make  clear,  in  particular  instances, 


548  A  TEXT-BOOK  OF  LOGIC 

in  which  of  these  two  ways  the  disjunctive  major 
is  to  be  interpreted,  we  are  likely  to  be  led  to  a  con- 
clusion which  leaves  us  in  doubt  as  to  the  meaning 
of  that  conclusion.  If  we  argue,  for  instance,  that 
'Because  all  male  students  of  the  university  either 
drill,  or  play  football,  or  baseball  or  tennis,  and  be- 
cause X  drills,  therefore,  he  does  not  play  football 
or  baseball  or  tennis/  we  are  stating  a  conclusion 
of  the  individual  which  may  be  true,  but  it  is  not 
true  for  the  reason  assigned;  for  there  is  nothing 
in  the  universe  of  physical  education  as  conducted 
by  the  university  that  makes  an  exclusive -interpre- 
tation of  the  enumerated  alternatives  necessary.  If, 
then,  we  give  an  exclusive  interpretation  to  a  non- 
exclusive series  of  alternatives,  or  a  non-exclusive 
interpretation  to  an  exclusive  series,  we  are  guilty 
of  the  fallacy  of  ambiguous  disjunction. 

REFERENCES 

SEE  THE  END  OF  THE  NEXT  CHAPTER 

QUESTIONS 

1.  What  is  the  name  and  character  of  Aristotle's  treatise 
on  fallacies? 

2.  In  what  senses  is  the  term  fallacy  used  at  the  present 
time? 

3.  In  what  two  main  groups  did  Aristotle  classify  the  fal- 
lacies? 

4.  To  what  distinctions  drawn  in  the  text  do  Aristotle's 
main  groups  correspond? 

5.  Describe  the  chief  features  of  each  of  the  four  main 
classes  into  which  the  text  divides  fallacies,  and  by  what 
names  are  they  distinguished? 


FALLACIES  549 

6.  Into  what   subdivisions,   and   according  to   what  prin- 
ciple, may  the  fallacies  of  interpretation  be  divided? 

7.  What  do  understand  by  verbal  ambiguity,  and  how  does 
it  differ  from  mere  indetterminateness  in  the  meaning 
of  words? 

8.  Describe  and  illustrate  the  fallacy  of  equivocation. 

9.  What  is  the  fallacy  of  accent,  and  in  what  respect  does 
the  corresponding  Greek  fallacy  differ  from  it? 

10.  In  what  several  ways  may  one  fall  into  a  fallacy  of 
accent?    Illustrate. 

11.  Describe  and  illustrate  the  fallacies  of  composition  and 
division. 

12.  What  is  the  Latin  name  for  the  fallacy  of  accident? 
Illustrate  the  fallacy. 

13.  Give  an  illustration  of  the  converse  fallacy  of  accident, 
and  by  what  Latin  name  is  it  known? 

14.  Describe  the  character  of  structural  ambiguity. 

15.  What  is  the  fallacy  of  amphibole,  and  from  what  other 
kinds  of  ambiguity  must  it  be  distinguished? 

16.  State  and  illustrate  the  fallacy  of  false  parenthesis. 

17.  What   do   you   understand   by   fallacies   of  implication, 
and  into  what  two  classes  may  they  be  divided? 

18.  What  is  a  fallacy  of  opposition? 

19.  To  what   fallacies   are  the   following   logical   relations 
particularly   liable:    contrariety,   subcontrariety,   subal- 
ter  nations? 

20.  What  is  a  fallacy  of  education? 

21.  State  what  is  meant  by  a  fallacy  of  obversion. 

22.  What  is  a  fallacy  of  conversion,  and  in  respect  of  what 
propositions,  and  why,  is  it  likely  to  occur? 

23.  What   are   fallacies   of   inference,   and   into   what   two 
classes  may  they  be  divided? 

24.  What  is  a  deductive  fallacy,  and  how  are  such  fallacies 
classified? 

25.  What  is  a  categorical  fallacy? 

26.  What  is  meant  by  a  fallacy  of  four  terms,  and  state  in 
what  two  ways  such  fallacies  arise 


550  A  TEXT-BOOK  OF  LOGIC 

27.  Classify  and  describe  each  of  the  fallacies  of  four  terms. 

28.  What  are  fallacies  of  insufficient  premises,  and  what 
rules  of  the  syllogism  do  they  break? 

29.  Show,  in  relation  to  the  nature  of  syllogistic  reasoning, 
how  the  fallacies  of  particular  and  of  negative  premises 
occur. 

30.  Describe  as  fully  as  you  can  the  character  of  an  hypo- 
thetical fallacy. 

31.  State  and  illustrate  the  two  hypothetical  fallacies. 

32.  How   does   the  fact   that   natural   events   are   complex 
affect  our  interpretation  of  hypothetical  statements? 

33.  What  do  you  understand  by  a  disjunctive  fallacy? 

34.  Into  what  classes,  and  according  to  what  principle,  may 
disjunctive  fallacies  be  divided? 

35.  State  and  illustrate  the  fallacy  of  false  disjunction. 

36.  Describe  the  fallacy  of  incomplete  disjunction.     Illus- 
trate. 

37.  What  is  the  fallacy  of  ambiguous  disjunction?     Illus- 
trate. 

EXERCISES 

Examine  the  following  arguments  and  state  in  what  respect, 
if  any,  they  are  fallacious,  the  technical  name  of  the 
fallacy  of  which  each  is  guilty,  and  the  class  to  which 
the  fallacy  belongs: 

(1)  It  is  sometimes  argued  that  the  communication  of 
an  infectious  disease  to  another  person  should  be 
punished  by  law,  since  the  law  exists  for  the  pur- 
pose of  protecting  people  from  harm. 

(2)  I  have  made  thee  free  a  slave. 

(3)  How  can  you   argue  that  it  is  wrong  for  me  to 
assist  my  friend  to  obtain  the  office  by  offering 
business  or  financial  considerations  to  the  voters 
of  my  acquaintance  if  you  agree  that  it  is  right 
for  a  man  to  do  what  he  can  for  his  friend's  good? 

(4)  A  commercial  traveller  wrote  to  his  chief:     Dear 
Sir,  On  Wednesday  next  I  want  you  to  allow  me 


FALLACIES  551 

the  day  off.  My  wife  having  lost  her  mother  is 
being  buried  on  that  date  and  I  should  like  to  at- 
tend the  funeral. 

(5)  A,  B,  C,  are  all  the  known  instances  of  the  class 
X,   and   since  they   are   all   found   to   possess  the 
characteristic  p  we  may  conclude  that  All  X  is  p. 

(6)  Large  numbers,  though  not   all,  of  the  instances 
of  the  class  X  have  invariably  been  found  to  ex- 
hibit the  character  p,  therefore,  All  X  is  p. 

(7)  If  it  is  false  that  no  men  are  immortal,  it  must 
certainly  be  true  that  all  men  are  mortal,  since 
there  is  no  middle  position  between  mortal  and  im- 
mortal. 

(8)  If  you  perform  an  unfriendly  act,  I  may  certainly 
conclude  that  your  attitude  is  hostile. 

(9)  He  who  is  content  with  what  he  has  is  truly  rich, 
but  the  covetous  man  is  not  content  with  what  he 
has,  no  covetous  man,  therefore,  is  truly  rich. 

(10)  All  Parisians  are  Frenchmen  indeed,  when  the  only 
reason  you  have  to  advance  for  that  statement  is 
that  all   Parisians  and   all  Frenchmen  are  Euro- 
peans ! 

(11)  What  is  not  compound  is  an  element,  gold  is  not 
compound,  and  is,  therefore,  not  an  element. 

(12)  If  a  substance  is  a  metal,  it  is  a  good  conductor 
of  heat  and  electricity,  but  this  substance  does  not 
conduct  either  well,  and  so  it  cannot  be  a  metal. 

(13)  If  man  were  not  capable  of  progress,   he  would 
not  differ  from  the  brutes,  but  since  he  does  differ 
he  must  be  regarded  as  capable  of  progress. 

(14)  What  you  speak  of  must  be  either  blue  or  green 
or  yellow,  but  since  you  say  that  it  is  neither  of 
these  it  must  be  devoid  of  colour. 

(15)  That  happened  on  Monday  or  Thursday  or  in  April, 
but  it  was  not  in  April  for  I  remember  that  it  was 
Harvest;    it   must,   therefore,    have   happened    on 
Monday  or  Thursday. 


CHAPTER  XIX 

FALLACIES    (CONTINUED) 

Inductive  Fallacies.  By  fallacies  of  induction, 
as  was  stated  above,  we  understand  those  errors  to 
which  thought  is  exposed  in  its  endeavour  to  deter- 
mine the  principle  of  connection  between  a  number 
of  particular  facts.  Now,  since  induction  requires, 
as  a  condition  of  the  explanation  of  the  particulars 
of  experience,  that  the  facts  of  experience  be  care- 
fully observed,  it  is  obvious  that  we  are  exposed 
mainly  to  two  classes  of  inductive  error,  to  those, 
namely,  which  arise  in  connection  with  our  obser- 
vation of  facts,  and  to  those  which  arise  in  connec- 
tion with  our  explanation  of  facts.  But  since  lan- 
guage is  an  indispensible  instrument  both  for  record- 
ing what  we  observe,  and  for  stating  the  methods 
and  results  of  the  explanations  that  we  have  to  offer 
of  what  is  observed,  we  may  include  in  the  present 
discussion  a  brief  statement  of  the  nature  and 
sources  of  the  fallacies  into  which  a  careless  use  of 
language  may  be  the  means  of  leading  us.  The  fal- 
lacies of  induction  will,  then,  be  studied  under  three 
heads ;  first,  those  which  originate  in  our  use  of  lan- 
guage; second,  those  which  involve  errors  of  obser- 
vation; and  third,  those  which  occur  in  connection 
with  the  so-called  inductive  inference,  the  errors, 
that  is  to  say,  which  invalidate  explanation. 

(552) 


FALLACIES  553 

Fallacies  of  Language.  Readers  of  Plato  cannot 
fail  to  have  remarked  that  the  difficulties  that  he 
sometimes  experienced  in  making  clear  to  himself 
and  to  others  the  character  of  some  of  the  more 
elementary  logical  distinctions  was  due,  in  great 
measure,  to  the  fact  that  the  nature  of  even  simple 
grammatical  distinctions  was  not  clearly  under- 
stood by  him  and  his  contemporaries.  The  fact 
that  Aristotle  attributed,  as  we  have  seen,  a  large 
number  of  the  fallacies  to  the  influence  of  language, 
also  points  to  the  close  connection  that  there  is 
between  thought  and  human  speech.  In  more  mod- 
ern times,  Bacon,  Hobbes,  Locke,  and  others,  have 
remarked  upon  the  dangers  to  which  we  are  liable 
through  the  words  that  we  employ  to  express  our 
ideas,  and  Mill  wrote  two  chapters  in  which  he 
discusses  the  requirements  and  principles  of  what 
he  calls  a  "philosophical  language."  These  refer- 
ences, which  might  be  indefinitely  extended,  are 
enough  to  show  that  while  our  acquired  speech 
may  be  sufficient  for  the  ordinary  purposes  of  life, 
it  must  be  carefully  employed  if,  in  regard  to  the 
subjects  of  scientific  investigation,  it  is  not  to  become 
a  source  of  embarrassment  and  error. 

Bacon  gave  the  name  of  Idols  of  the  Market- 
place (Idola  fori)  to  the  fallacies  which  were  due 
to  language,  and  he  puts  the  sum  of  the  matter  as 
follows:  "Men  imagine  that  their  reason  governs 
words  whilst,  in  fact,  words  react  upon  the  under- 
standing; and  this  has  rendered  philosophy  and  the 
sciences  sophistical  and  inactive."  The  same  truth 


554  A  TEXT-BOOK  OF  LOGIC 

is  dwelt  upon  at  length  by  Locke,  and  the  general 
nature  of  the  influence  that  language  is  capable  of 
exerting  prejudicially  upon  thought,  the  only  point 
with  which  we  are  here  concerned,  is  evident  from 
the  following  quotation:  "Men,"  he  says,  "having 
been  accustomed  from  their  cradles  to  learn  words 
which  are  easily  got  and  retained,  before  they  knew 
or  had  framed  the  complex  ideas  to  which  they  were 
annexed,  or  which  were  to  be  found  in  the  things 
they  were  thought  to  stand  for,  they  usually  con- 
tinue to  do  so  all  their  lives;  and,  without  taking 
the  pains  necessary  to  settle  in  their  minds  deter- 
mined ideas,  they  use  their  words  for  such  unsteady 
and  confused  notions  as  they  have,  contenting  them- 
selves with  the  same  words  other  people  use,  as  if 
their  very  sound  necessarily  carried  with  it  con- 
stantly the  same  meaning.  .  .  .  This  inconsistency 
in  men's  words  when  they  come  to  reason  concerning 
either  their  tenets  or  interest,  manifestly  fills  their 
discourse  with  abundance  of  empty,  unintelligible 
noise  and  jargon,  especially  in  moral  matters,  where 
words,  for  the  most  part,  standing  for  arbitrary 
and  numerous  collections  of  ideas  not  regularly  and 
permanently  united  in  nature,  their  bare  sounds  are 
often  only  thought  on,  or  at  least  very  obscure  and 
uncertain  notions  annexed  to  them.  Men  take  the 
words  they  find  in  use  amongst  their  neighbours; 
and,  that  they  may  not  seem  ignorant  what  they 
stand  for,  use  them  confidently,  without  much 
troubling  their  heads  about  a  certain  fixed  meaning ; 
whereby,  besides  the  ease  of  it,  they  obtain  this 


FALLACIES  555 

advantage:  That,  as  in  such  discourses  they  seldom 
are  in  the  right,  so  they  are  as  seldom  to  be  con- 
vinced that  they  are  in  the  wrong;  it  being  all  one 
to  go  about  to  draw  those  men  out  in  their  mistakes 
who  have  no  settled  notions,  as  to  dispossess  a 
vagrant  of  his  habitation  who  has  no  settled  abode." 
Fallacies  of  Observation.  Observation  may  be 
defective  chiefly  in  two  respects.  It  may  be  insuffi- 
cient in  amount,  or  incomplete  or  imperfect  in 
detail.  If  we  consider  these  two  cases  separately,  it 
must  not  be  forgotten  that,  frequently  and  perhaps 
usually,  the  fallacies  which  depend  upon  observation 
occur  as  the  result  of  both  kinds  of  defect.  Induc- 
tion, as  we  have  seen,  depends  upon  the  collection 
of  data  sufficient  in  amount  to  suggest  a  law  of  con- 
nection; but,  more  important  than  the  number  of 
the  facts  observed,  is  the  degree  of  thoroughness 
with  which  we  are  able  to  analyse  them.  Mere  col- 
lections of  fact,  if  such  a  thing  were  possible,  have, 
as  we  have  seen,  no  special  value  for  science,  and 
alone  can  lead  to  the  formulation  of  no  general 
principles  of  connection.  The  particular  data  which 
are  the  material  of  science  are  brought  under  obser- 
vation by  the  exercise  of  discrimination,  comparison, 
synthesis,  in  a  word,  judgment;  and  this  differs 
in  no  essential  respects  from  the  process  by  which 
we  detect,  within  collected  groups  of  fact,  the  fea- 
tures that  are  common,  and  the  connections  that 
are  causal.  But  while  this  should  be  kept  clearly  in 
mind,  it  is  nevertheless  true  that  we  may  be  led  into 
an  inductive  fallacy,  either  because  the  amount  of 


556  A  TEXT-BOOK  OF  LOGIC 

data  available  does  not  warrant  an  inference,  or 
because,  although  sufficient  in  amount,  our  analysis 
of  the  data  has  not  been  carried  out  with  sufficient 
care  and  thoroughness. 

Observation,  then,  is  defective,  in  the  first  place, 
when  the  number  of  the  observed  data  is  not  suffi- 
cient in  amount  to  guarantee  the  conclusion  that  is 
based  upon  it.  In  view  of  the  situations  which  this 
statement  has  in  view,  we  are  particularly  inter- 
ested, in  logic,  to  ascertain  what  are  the  conditions 
that  lead  to  insufficient  observation.  One  important 
condition  is  the  general  tendency  to  neglect  the 
observation  and  collection  of  what  are  called  nega- 
tive instances.  By  a  negative  instance  is  meant  an 
instance  in  which  a  given  phenomenon  is  observed 
not  to  occur.  If  we  take,  for  example,  the  popular 
superstitions,  —  such,  for  instance,  that  it  is  un- 
lucky to  begin  any  new  task  or  undertake  any  new 
enterprise  on  Friday,  for  people  to  be  associated 
together  in  groups  of  thirteen,  or  to  walk  under  a 
ladder  that  is  inclined  against  a  wall,  —  we  are 
seriously  expected,  by  those  who  entertain  them,  to 
share  these  superstitions  in  view  of  the  instances 
that  these  persons  are  able  to  enumerate  in  which 
some  untoward  result  has  occurred.  An  enumer- 
ation of  the  instances  in  which  no  such  consequence 
has  followed,  it  would  seem,  is  sufficient  to  show  that 
the  superstitituous  conclusion  is  defective  if  not 
fallacious  by  reason  of  the  failure  to  observe  these 
negative  instances. 


FALLACIES  557 

To  have  called  our  attention  to  this  tendency  to 
neglect  the  evidence  afforded  by  negative  instances 
is  one  of  the  merits  of  Bacon.  The  following  quo- 
tation from  the  Novum  Organum,  not  only  states 
the  nature  of  the  fallacy,  but  indicates  also  its  scope. 
Bacon  writes:  "The  human  understanding,  when 
any  proposition  has  been  once  laid  down  (either 
from  general  admission  and  belief  or  from  the 
pleasure  it  affords),  forces  everything  else  to  add 
fresh  support  and  confirmation;  and  although  most 
cogent  and  abundant  instances  may  exist  to  the  con- 
trary, yet  either  does  not  observe  or  despises  them, 
or  gets  rid  of  and  rejects  them  by  some  distinction, 
with  violent  and  injurious  prejudice,  rather  than 
sacrifice  the  authority  of  its  first  conclusions.  It 
was  well  answered  by  him  who  was  shown  in  a 
temple  the  votive  tablets  suspended  by  such  as  had 
escaped  the  peril  of  shipwreck,  and  was  pressed  as 
to  whether  he  would  then  recognise  the  power  of 
the  gods :  But  where  are  the  portraits  of  those  who 
have  perished  in  spite  of  their  vows?  All  super- 
stition is  much  the  same,  whether  it  be  that  of 
astrology,  dreams,  omens,  retributive  judgment,  or 
the  like,  in  all  of  which  the  deluded  observers 
observe  events  which  are  fulfilled,  but  neglect  and 
pass  over  their  failure,  though  it  be  much  more 
common.  But  this  evil  insinuates  itself  still  more 
craftily  in  philosophy  and  the  sciences,  in  which  a 
settled  maxim  vitiates  and  governs  every  other  cir- 
cumstance, though  the  latter  be  much  more  worthy 
pf  confidence.  Besides,  even  in  the  absence  of  that 


558  A  TEXT-BOOK   OF  LOGIC 

eagerness  and  want  of  thought  (which  we  have 
mentioned),  it  is  the  peculiar  and  perpetual  error 
of  the  human  understanding  to  be  more  moved  and 
excited  by  affirmatives  than  by  negatives,  whereas 
it  ought  duly  and  regularly  to  be  impartial ;  nay,  in 
establishing  any  true  axiom  the  negative  instance 
is  the  more  powerful." 

The  testimony  of  Darwin  is  to  the  same  effect. 
He  says :  "The  success  of  the  'Origin'  may,  I  think, 
be  attributed  in  large  part  to  my  having  long  before 
written  two  condensed  sketches,  and  to  my  having 
abstracted  a  much  larger  manuscript,  which  was 
itself  an  abstract.  By  this  means  I  was  enabled  to 
select  the  more  striking  facts  and  conclusions.  I 
had  also,  during  many  years,  followed  a  golden  rule 
—  namely,  whenever  a  published  fact,  a  new  obser- 
vation or  thought,  came  across  me,  which  was  op- 
posed to  my  general  results,  to  make  a  memorandum 
of  it  without  fail  and  at  once;  for  I  had  found  by 
experience  that  such  facts  and  thoughts  were  far 
more  apt  to  escape  from  memory  than  favourable 
ones.  Owing  to  this  habit,  very  few  objections  were 
raised  against  my  views  which  I  had  not  at  least 
noticed  and  attempted  to  answer." 

Another  condition  of  insufficient  observation 
that  may  be  mentioned  is  education.  Whatever  our 
conception  of  the  aim  of  education  may  be,  there  is 
no  doubt  that  a  large  part  of  the  educative  process, 
as  we  actually  experience  it,  is  taken  up  with  an 
effort  to  gain  familiarity  with  a  body  of  knowledge 
that  is  regarded  as  traditionally  important  and  fun- 


FALLACIES  559 

mental.  This  statement  is  true  for  all  grades  of 
education  from  the  grammar  school  to  the  univer- 
sity. Now  it  is  not  only  inconceivable,  but  contrary 
to  experience,  that  the  acquisition  of  any  con- 
erable  body  of  knowledge  should  be  without  its 
effect  upon  our  mental  habits;  for  acquaintance 
with  any  class  of  facts  means,  in  terms  of  men- 
tal habit,  a  trained  ability  to  perceive  with  in- 
creasing facility  other  facts  that  are  the  same  in 
kind  as  these,  and  a  corresponding  inability  to  per- 
ceive facts  that  differ  considerably  from  them  in 
kind.  A  particular  illustration  of  this  general  truth 
is  found  in  the  case  of  those  individuals  whose  edu- 
cation assumes  a  special  character,  as  it  does,  for 
instance,  in  law,  medicine,  theology,  engineering, 
etc.  And  even  if  we  consider  the  case  of  those 
whose  common  school  education  is  not  followed  by 
a  university  training,  but  by  apprenticeship  in  some 
business,  it  is  quite  apparent,  even  then,  that  the 
knowledge  of  the  business,  of  its  material,  methods, 
and  aims,  acts  exactly  in  the  same  way  to  sharpen 
the  perception  to  observe  a  specialised  group  of 
facts,  and  to  limit  the  facility  with  which  facts 
dissimilar  to  these  are  perceived.  The  truth  is 
that  all  of  us  perceive  what  we  are  educated  to 
perceive,  and  that  we  are  limited  in  respect  to  the 
kinds  of  things  that  we  perceive  by  the  education 
that  we  have  received. 

Bacon  referred  to  the  errors  into  which  we  are 
led  as  the  result  of  the  limitations  that  education 
and  inherited  beliefs  may  have  upon  the  range  of 


560  A  TEXT-BOOK   OF  LOGIC 

our  perceptions  as  Idols  of  the  Theatre  (Idola  The- 
atri) .  Doubtless,  as  is  shown  by  his  illustrations, 
he  had  in  mind  the  cramping  effect  of  the  traditions 
of  the  Schoolmen  upon  the  new  learning  in  his  day. 
Bacon  lived  at  the  dawn  of  the  modern  scientific 
era,  and  he  was  acquainted  with  some  of  the  ob- 
stacles that  it  had  to  encounter  on  account  of  theo- 
logical prejudice  (odium  theologicum)  of  the  times. 
But  if  we  have  passed  beyond  the  stage  where  the 
prejudices  which  come  from  a  one-sided  theological 
position  and  training  are  allowed  to  interfere  with 
the  freedom  of  thought  and  investigation,  it  is  still 
possible  that  prejudices  the  same  in  kind,  though 
different  in  form,  may  hamper  the  human  mind  in 
its  search  for  truth.  The  fact  that  these  hindrances 
are  not  officially  administered,  but  are  grounded  in 
that  specialisation,  upon  which  our  modern  educa- 
tion lays  so  much  importance,  would  make  the  ten- 
dency to  which  we  are  referring  the  more  insidious, 
and  hence  more  difficult  to  detect  and  avoid  or  over- 
come. "The  success  of  modern  scientific  methods," 
as  Creighton  remarks,  "has  sometimes  led  investi- 
gators to  despise  and  belittle  the  work  of  those  who 
do  not  carry  on  their  investigations  in  laboratories, 
or  do  not  weigh  and  measure  everything."  Thus 
the  mechanical  conceptions  which  were  worked  out 
successfully  in  the  realm  of  physics  and  astronomy, 
have  been  extended  to  psychology,  ethics,  and  polit- 
ical science,  without  any  consideration  being  given 
to  the  differences  in  the  material  which  is  the  sub- 
ject-matter of  this  latter  group  of  sciences.  In  our 


FALLACIES  561 

own  day,  the  evolutionary  hypothesis  has  provided 
us  with  a  point  of  view  for  looking  at  all  the  details 
of  human  experience;  but  it  is  not  impossible  that 
the  limitations  of  this  point  of  view  and  the  errors  of 
observation  to  which  it  has  led,  may,  at  some  future 
time,  be  as  clear  as  today  are  the  insufficiencies  of 
the  notion  of  mechanism  as  employed  by  the  thinkers 
of  the  eighteenth  century. 

In  the  second  place,  observation  may  be  defective 
either  because  it  is  incomplete  or  imperfect  in  detail. 
The  instances  of  fallacious  inference  which  belong 
in  this  group  are  those  which  arise  from  the  fact 
that  the  collected  data,  upon  which  the  inferences 
rest,  have  not  been  examined  with  sufficient  thor- 
oughness. Defects  of  the  kind  here  in  question  may 
be  due  either  to  the  fact  that  only  part  of  the  mate- 
rial has  been  studied,  or  to  the  fact  that,  while  all 
the  material  may  have  been  studied,  this  has  not 
been  done  for  all  or  parts  of  the  material  with  suffi- 
cient minuteness.  In  either  case,  the  inference  will 
be  erroneous  on  account  of  a  failure  to  carry  our 
analysis  of  the  phenomenon  under  observation  into 
sufficient  detail. 

A  number  of  conditions  may  operate  to  arrest 
our  analysis  of  observed  data  at  a  point  which  falls 
short  of  that  at  which  it  is  possible  to  determine 
with  some  degree  of  accuracy  the  law  of  their 
connection,  but  two  are,  from  the  logical  point 
of  view,  of  sufficient  interest  to  require  brief  men- 
tion. There  is  no  doubt,  in  the  first  place,  that  great 


562  A  TEXT-BOOK  OF  LOGIC 

differences  exist  in  the  ability  of  different  investi- 
gators to  perform  the  task  of  analysing  a  group  of 
collected  facts.  Some  individuals,  it  is  found,  are 
splendid  collectors,  and  are  exceedingly  fertile  in 
devising  ways  and  means  of  bringing  under  obser- 
vation specimens  that  entirely  escape  the  notice  of 
others  not  gifted  as  themselves.  But  it  sometimes 
happens  that  among  these  born  collectors  there  are 
many  who  can  go  but  a  little  way  toward  that  com- 
plete analysis  of  their  collected  material  upon  which 
alone  any  general  conclusion  can  safely  be  based. 
The  recognition  of  this  fact  has  led,  in  practice,  to 
the  introduction  of  a  large  amount  of  cooperation 
between  workers  in  the  same  line  of  research,  and 
has  tended  to  make  the  laboratory  a  workship  in 
which  there  is  found  employment  for  a  great  variety 
of  talent.  It  is  only  the  exceptional  man  who,  like 
Darwin,  combines  the  collector's  skill  with  a  keen 
analytic  mind  that  brings  to  light  the  common  fea- 
tures that  lie  hidden  under  a  mass  of  differences  in 
any  group  of  facts.  Natural  limitations,  then,  of 
the  sort  we  are  discussing  operate  frequently  to 
render  the  observation  of  details  incomplete,  and  to 
throw  doubt  upon  any  conclusion  which  rests  upon 
such  imperfectly  analysed  data. 

Another  condition  which  tends  to  make  analysis 
defective  is  an  imperfectly  developed  technique  or 
method.  We  have  spoken  above  of  the  importance 
of  the  construction  and  use  of  apparatus  if  the  work 
of  scientific  observation  is  to  be  successfully  carried 
on.  Indeed,  we  may  say  that  the  progress  of  modern 


FALLACIES  563 

science  has  been  dependent,  in  large  measure,  on 
the  success  that  has  attended  the  development  of 
special  methods  for  bringing  the  structure  of  col- 
lected data  under  detailed  observation.  In  the  bio- 
logical sciences,  for  example,  the  methods  of  hard- 
ening, embedding,  and  staining  the  various  tissues 
have  gone  a  long  way  toward  placing  these  sciences 
on  the  same  experimental  plane  as  physics  and 
chemistry.  The  further  progress  of  these,  as  of  the 
other,  sciences  depends  upon  the  adaptation  of  the 
methods  already  in  vogue  to  new  material,  and  the 
development  of  new  methods  to  meet  new  conditions 
and  situations  as  they  arise.  But  whenever  we 
speak  of  improvement,  and  recognise  the  possibility 
of  new  discoveries,  we  at  the  same  time  imply  that 
our  present  knowledge  is  defective  in  just  those 
respects  in  which  advancement  may  be  expected. 
This,  however,  is  only  to  say  that  so  long  as  the 
technique  of  any  science  is  capable  of  improvement, 
the  conclusions  of  that  science  must  be  entertained 
with  caution  and  subject  to  certain  reservations. 

Fallacies  of  Explanation.  There  are  two  sources 
of  error  in  inductive  processes  of  reasoning  to  which 
we  shall  direct  attention:  hasty  generalisation  and 
false  analogy.  It  is  exceedingly  difficult  to  give  a 
concise  statement  of  what  is  meant  by  hasty  general- 
isations, since  any  explanation  may  be  rendered 
erroneous  by  undue  haste  at  any  of  the  stages  of  the 
inductive  process.  For  instance,  an  inductive  con- 
clusion may  be  fallacious  on  account  of  haste  at 
either  the  stage  of  what  was  called  above  empirical 


564  A  TEXT-BOOK  OF  LOGIC 

generalisation,  or  at  the  stage  of  hypothesis,  or  at 
the  stage  of  verification.  Whenever,  therefore,  any 
part  of  the  task  of  explanation  is  not  thoroughly 
performed,  our  conclusion,  resting  as  it  does  upon 
an  incomplete  or  imperfect  acquaintance  with  the 
details  of  the  phenomenon,  may  be  called  a  hasty 
or  premature  generalisation.  The  essential  nature 
of  the  fallacy  consists,  then,  in  the  absence  of  an 
analytic  thoroughness  requisite  for  a  true  explana- 
tion, without  respect  to  the  part  of  the  explanatory 
process  in  which  the  failure  to  be  sufficiently  thor- 
ougs  occurs. 

We  may  remark,  however,  that  we  are  not  guilty 
of  this  fallacy  when  we  consciously  arrest  our  anal- 
ysis of  a  phenomenon  to  be  explained  at  a  point 
which  falls  short  of  completeness,  or  when  imper- 
fectly observed  or  analysed  data  are  generalised, 
but  are  not  offered  as  an  explanation.  The  fallacy 
occurs  only  when  an  incomplete  analysis  is  presumed 
to  be  complete,  or  when  a  preliminary  generalisation 
is  mistaken  for  a  final  one.  As  has  been  said,  the 
value  of  logic  consists  in  calling  attention  to  the  fact 
that,  not  only  must  conclusions  be  true,  but  the 
reasons  for  the  truth  of  conclusions  must  be  defi- 
nitely ascertained,  if  science  is  to  exist.  Science,  as 
we  have  seen,  is  a  consciously  controlled  process,  a 
process  of  arriving  at  a  certain  conclusion,  by  means 
of  a  method;  which  is  definitely  regulated  at  all  the 
stages  through  which  it  passes  from  the  earliest 
observation  to  the  finally  accepted  explanation. 
When  the  control  of  the  method  by  which  conclu- 


FALLACIES  565 

sions  are  reached  gets  out  of  hand,  when  we  become 
careless  in  the  use  of  the  methods  we  adopt  for  the 
examination  of  phenomena,  our  explanation  of  such 
phenomena  is  erroneous,  because  it  involves,  in  the 
sense  in  which  the  term  has  been  explained,  a  hasty 
generalisation.  Such  conclusions  are  fallacious  be- 
cause they  do  not  rest  upon  a  sufficiently  detailed 
basis  of  fact. 

Analogy  may  give  rise  to  erroneous  conclusions 
when  it  is  supposed  that  the  phenomenon  under 
observation  has  all  the  characteristics  of  the  instance 
which  provides  us  with  the  analogical  resemblance. 
We  have  seen  that  analogy  is  a  useful  method,  or 
step  in  the  method,  of  scientific  explanation,  but 
unless  it  is  strictly  guarded  it  is  likely  to  arouse  all 
sorts  of  distracting  associations  which  lead  to  mis- 
understanding and  error.  When  considered  as  a 
possible  source  of  error,  analogy  has  certain  affin- 
ities with  figurative  language,  on  the  one  hand,  and 
with  the  disregard  of  negative  instances,  on  the 
other.  With  respect  to  its  relation  to  figurative 
language,  analogy  leads  us  astray  when  the  illustra- 
tion which  provides  us  with  the  analogical  resem- 
blance engages  the  whole  attention,  and  we  are 
thereby  led  to  predicate  of  the  phenomenon  under 
investigation  qualities  that  have  been  actually  ob- 
served only  in  the  illustration.  It  was  with  the  dan- 
gers of  analogical  reasoning  in  mind  that  a  professor 
was  wont  to  say  to  his  students  that  they  should 
not  try  to  make  the  parables  of  the  New  Testament 
"go  on  all  fours,"  that  is,  they  must  not  try  to  find 


566  A  TEXT-BOOK   OF  LOGIC 

a  point  for  point  resemblance  between  the  truth  of 
the  parable  and  the  story  which  provided  the  basis 
of  the  analogy.  It  is  neglect  of  such  counsel  that 
leads  in  the  sciences  to  the  fallacy  of  false  analogy. 
With  respect  to  its  relation  to  negative  instances, 
analogy  is  likely  to  lead  us  into  error  if  the  points 
of  difference  between  a  phenomenon  and  its  illus- 
tration are  lost  sight  of,  and  only  the  resemblances 
are  retained.  "For  instance,"  to  borrow  an  illus- 
tration from  Sidgwick,  "during  the  recent  Boer 
War  various  analogies  were  appealed  to  by  various 
people  as  helping  to  throw  light  on  the  situation. 
It  was  compared  to  the  operations  of  America  in 
the  Philippines,  to  the  Armenian  massacres,  to  the 
American  Civil  War,  and  even  to  the  high-handed 
action  of  Spain  in  the  Netherlands  in  the  time  of 
Elizabeth.  Our  action  in  South  Africa  was  sup- 
posed (by  different  people)  to  be  analogous  to  those 
and  other  historical  precedents,  and  the  analogies 
were  used  to  support  the  various  judgments  passed 
by  these  various  people  on  the  rights  of  the  war  and 
its  probable  outcome.  It  is  easy  to  see  that  in  all 
these  comparisons  there  is  some  likeness  and  also 
some  difference,  and  that  the  justice  of  the  analogy 
depends  upon  the  relevance  of  the  likeness  and  the 
difference."  But  if  the  difference  is  a  relatively 
important  one,  and  we  proceed  nevertheless  to  build 
up  an  explanation  on  the  ground  of  the  likeness 
alone,  we  are  guilty  of  the  fallacy  of  false  analogy. 
The  fallacy  assumes  the  converse  form  if  we  are  led 
to  underestimate  the  value  of  a  resemblance  because 


FALLACIES  567 

it  is  accompanied  by  striking  differences.  In  any 
case,  the  fallacy  arises  when  we  forget  that  analog- 
ical reasoning  depends  upon  what  Sidgwick  calls 
"the  relevance  of  the  likeness  and  difference." 

Fallacies  of  the  Context.  The  fallacies  that  we 
have  considered  in  the  foregoing  pages  arise  out  of 
a  failure  to  determine  precisely  the  nature  and  rela- 
tions of  the  subject-matter  which  constitutes  the 
contents  of  particular  arguments.  The  group  of 
fallacies  to  which  we  have  now  to  direct  attention 
arises  from  the  fact  that  the  meaning  of  particular 
arguments,  as  we  have  shown,  is  determined  in  part 
by  their  relation  to  a  context  which  they  imply  with 
varying  degrees  of  clearness.  Now  when  we  say 
that  the  context  supplies  part  of  the  meaning  that 
an  argument  may  rightly  be  said  to  have,  it  is  im- 
portant to  bear  in  mind  that  the  context  may  be 
said  to  refer,  not  only  to  the  undetermined  aspects 
of  the  subject-matter  under  discussion,  but  also  to 
the  interests  or  purposes  which  sustain,  as  we  have 
seen,  our  inquiries  into  truth  and  our  search  for 
knowledge.  Any  discussion  of  what  knowledge  or 
truth  is  cannot  fail  to  be  inadequate,  as  we  have 
shown,  if  attention  is  not  given  to  the  part  played 
by  the  complex  character  of  the  material  about 
which  knowledge  is  desired,  and  also  to  the  character 
of  the  interest  which  knowledge  is  intended  to  sat- 
isfy. Because,  therefore,  of  its  relation  to  a  context, 
every  argument  is  liable  to  errors  which  do  not  arise 
directly  out  of  the  facts  and  relations  which  are 
expressed  by  its  constituent  propositions.  There 


568  A  TEXT-BOOK  OF  LOGIC 

may  be  imported,  that  is  to  say,  into  the  meaning 
of  arguments  elements  from  their  contexts  which 
lead  to  conclusions  which  are  at  variance  with  what 
the  premises,  logically  interpreted,  really  support. 
Whenever  this  happens,  whenever,  that  is,  we  accept 
arguments  on  the  ground  of  suggestions,  derived 
from  their  contexts,  which  are  not  related  to  the 
truth  character  of  the  arguments  themselves,  there 
ensues  a  fallacy  of  the  context.  A  fallacy  of  the 
context  may  be  defined,  therefore,  as  an  error  in 
reasoning  which  is  due  to  the  influence  that  some 
feature  or  features  of  a  context,  not  related  to  the 
truth  character  of  the  argument,  has  upon  our  inter- 
pretation of  the  subject-matter  of  the  argument, 
such  influence  inducing  us  to  accept  a  statement 
about  the  subject-matter  of  the  argument  as  true  for 
reasons  which,  apart  from  the  influence  referred  to, 
would  fail  wholly  or  in  part,  to  justify  its  accept- 
ance. 

The  nature  of  these  fallacies  may  be  made  still 
clearer,  if  we  observe  that  in  arguments  of  the  kind 
under  consideration  the  context  may  contribute 
irrelevant  elements  derived  from  either  of  the  fac- 
tors by  which,  as  was  pointed  out,  human  knowledge 
is  determined,  —  from  the  world  of  relatively  inde- 
pendent objects  on  the  one  hand,  and  from  the  world 
of  our  interests,  on  the  other.  An  imperfect  deter- 
mination of  the  universe  within  which  an  argument 
is  intended  to  be  considered  leads  to  a  group  of  fal- 
lacies of  which  Petitio  Principii,  Ignoratio  Elenchi, 
Non  Sequitur,  and  Complex  Question  are  the  chief; 


FALLACIES  569 

and  a  failure  to  confine  the  interests  by  which  we 
are  guided  in  our  search  for  truth  to  those  which 
have  a  direct  relation  to  that  end  leads  to  another 
group  of  which  Post  Hoc,  Argumenta  ad  Hominen, 
ad  Populum,  ad  Verecundiam,  ad  Misericordiam, 
may  be  taken  as  the  most  important.  In  the  former 
group,  we  are  considering  how  the  relations  which 
a  given  object  has  to  other  objects  may  become  a 
source  of  error  in  our  knowledge  of  the  world  of 
relatively  objective  things,  and  to  these  we  may  give 
the  name,  fallacies  of  assumption.  In  the  latter,  we 
are  studying  the  ways  in  which  knowledge  may  be 
deflected  by  reason  of  the  operation  of  certain  nat- 
ural and  acquired  characteristics  of  the  mental  life ; 
and  to  these  we  may  give  the  name,  fallacies  of 
interest.  In  both  cases  the  fallacy  is  due  to  the 
admission  into  our  reasoning  of  elements  which  have 
no  direct  bearing  upon  the  truth  character  of  the 
judgments  in  which  our  knowledge  is  asserted. 

Fallacies  of  Assumption  are  those  errors  in  rea- 
soning which  occur  when  the  assumptions  on  which 
an  argument  rests  are  not  clearly  distinguished  from 
the  judgments  of  which  the  argument  consists.  ^  An. 

^assumption,  in  this  connection,  is  anything  we  take 
for  granjejL-but  do  not  assert,  about  the  subject- 
matter  of  anjirgument.  It  is  the  equivalent  of  what 
we  have  had  occasion  hitherto  to  speak  of  as  the 
universe  of  discourse.  Interpreted  from  this  point 
of  vtewf  it  is  readily  seen  that  an  assumption  is  not 

<^afl-assertion.  and  forms  no  part  of  the  asserted  con- 
tents of  an  argument,  although,  as  we  have  seen,  it 


570  A  TEXT-BOOK  OF  LOGIC 

has  a  relation  to  the  argument,  a  relation  which  is 
indicated  with  sufficient  clearness  by  saying  that  it 
points  out  the  sphere  of  reference  in  which  what  is 
asserted  may  or  not  be  accepted.  Now  it  is  a  misin- 
terpretation of  the  relation  betweeji  what  an  argu- 
ment assumes  and  what  it  asserts  that  lies  at  the 
foundation  of  the  fallacies  that  we  have  here  to  con- 
sider. Thus,  when  what  is  taken  for  granted  or  as- 
sumed is  allowed  to  function  in  any  part  of  an  argu- 
ment as  an  assertion  or  judgment,  or  when  the  as- 
sumption on  which  an  argument  proceeds  is  ambig- 
uous, the  resulting  fallacy  is  one  of  assumption. 

Petitio  Princpii  is  the  name  of  an  argument  which 
assumes  the  conclusion  that  is  to  be  proved.  It  is, 
as  Sidgwick  says,  "the  surreptitious  assumption  of 
a  truth  you  are  pretending  to  prove."  Since,  then, 
the  fallacy  is  one  of  assumption,  it  is  evident  that 
its  source  must  be  found,  not  in  what  is  definitely 
asserted,  but  in  the  world  of  reality  or  existence  in 
which  what  is  asserted  has  a  definite  meaning  or 
fulfillment,  that  is  to  say,  in  the  universe  of  dis- 
course from  the  standpoint  of  which  the  argument 
is  interpreted.  The  nature  of  the  fallacy  is  seen  in 
the  confusion  that  exists,  for  the  person  guilty  of 
it,  between  the  asserted  grounds  of  a  conclusion, 
and  the  assumptions  that  thought  postulates  with 
respect  to  the  subject  -  matter  of  an  argument, 
Whenever  it  exists,  the  fallacy  directs  attention  to 
the  fact  that  the  truth  of  what  an  argument  asserts 
depends  in  part  upon  what  assumptions  the  argu- 
ment makes ;  and,  in  view  of  the  nature  of  an  argu- 


FALLACIES  571 

ment,  it  follows  that  when  assumptions  are  put 
forward  as  reasons  we  necessarily  fail  to  establish 
a  conclusion,  and  fall  into  the  merest  dogmatism 
unless  we  are  willing  to  have  these  assumptions 
called  into  question.  "When,"  for  instance,  "Galileo 
maintained  that  the  earth  goes  round  the  sun,  he 
fully  believed  it  and  yet  was  willing  to  treat  it  as  a 
disputable  question ;  but  when  Pope  Urban  VIII  and 
his  cardinals  maintained  that  the  earth  stood  still, 
they  shut  their  eyes  to  the  arguments,  and  said  their 
view  was  only  disputable  by  any  one  who  chose  to 
be  burnt  alive."  Now,  with  respect  to  the  right  to 
call  into  question  any  of  the  grounds  on  which  con- 
clusions are  supposed  to  rest,  we  can  only  say  that 
this  right  must  be  conceded,  or  that  the  fallacy  we 
are  now  considering  can  have  no  logical  standing. 
But  further,  if  we  cannot  go  behind  the  premises, 
nor  consider  ^e  rights  of  assertions  to  stand  as 
premises,  but  must  accept  any  set  of  assertions  at 
their  face  value  as  grounds  of  argument,  then  the 
whole  of  logic  has  been  reduced  to  a  mere  formal 
science,  and  its  processes  are  valuable  only  as  they 
enable  us  to  secure  consistency  of  statement.  Either 
this,  or  we  must  admit  that  there  is  a  real  difference 
between  assertions  and  assumptions,  between  judg- 
ments and  postulates,  that  the  human  mind  is  likely 
at  times  to  fail  to  keep  the  distinction  clearly  before 
it,  and,  consequently,  that  the  one  may  sometimes 
slip,  in  the  course  of  argument,  into  the  place  of  the 
other.  Now,  when  this  happens,  when  in  the  course 
of  argument  assumptions  take  the  place  of  reasoned 


572  A  TEXT-BOOK  OP  LOGIC 

judgments,  the  argument  is  fallacious  because,  for 
the  reason  assigned,  it  involves  a  petitio  principii. 

The  English  language,  as  Whately  pointed  out, 
is  peculiarly  "suitable  for  the  fallacy  of  Petitio 
Principii,  from  its  being  formed  from  two  distinct 
languages,  and  thus  abounding  in  synonymous  ex- 
pressions which  have  no  resemblance  in  sound,  and 
no  connection  in  etymology,  so  that  a  Sophist  may 
bring  forth  a  proposition  expressed  in  words  of 
Saxon  origin,  and  give  as  a  reason  for  it  the  very 
same  proposition  stated  in  words  of  Norman  origin ; 
e.  g.  To  allow  every  man  an  unbounded  freedom  of 
speech  must  always  be,  on  the  whole,  advantageous 
to  the  State ;  for  it  is  highly  conducive  to  the  inter- 
ests of  the  community,  that  each  individual  should 
enjoy  a  liberty  perfectly  unlimited  of  expressing 
his  sentiments/  * 

When  the  fallacy  of  petitio  principii  is  com- 
mitted in  a  single  step  it  is  called  vvrepov  irporepw 
(hysteron  proteron)  ;  and  when  it  involves  more 
than  a  single  step  it  is  called  circulus  in  probando  or 
reasoning  in  a  circle. 

Closely  connected  with  the  foregoing  is  the  fal- 
lacy of  the  Complex  Question.  By  a  complex  ques- 
tion, in  the  broadest  meaning  of  that  term,  is  meant 
one  that  suggests  its  own  answer.  Any  question, 
for  instance,  that  forces  us  to  select,  and  assert  in 
our  answer  to  it,  one  of  the  elements  of  the  question 
itself,  while  some  other  possibility  is  really  open,  is 
complex  in  the  sense  in  which  that  term  is  here  em- 
ployed. If,  for  example,  one  were  to  ask  whether 


FALLACIES  573 

you  were  going  to  New  York  or  London,  or  if  your 
favourite  colour  were  red  or  blue,  or  if  you  had 
given  up  a  particular  bad  habit,  he  would  be  guilty 
of  the  fallacy  of  the  complex  question,  if,  in  each 
case,  the  alternatives,  as  a  matter  of  fact,  were  more 
numerous  than,  or  were  in  any  way  different  from, 
those  stated  in  the  question.  Any  leading  question 
which  complicates  an  issue  by  over  simplification  is 
fallacious  for  the  same  reason.  Now,  in  the  light 
of  what  we  have  said  with  respect  to  the  petitio 
principii,  it  is  not  difficult  to  see  that  the  fallacy  of 
the  complex  question  is  occasioned  by  the  character 
of  the  assumption  on  which  the  question  rests.  In 
the  petitio  principii  an  assumption  with  respect  to 
the  subject-matter  of  an  argument  functions  as  a 
premise,  in  the  complex  question  it  is  a  similar  as- 
sumption that  shuts  out  some  of  the  material  possi- 
bilities of  a  situation  and  confines  an  issue  within 
too  narrow  limits.  As  in  the  former  case,  so  here, 
the  only  way  of  meeting  the  difficulty  is  to  raise  the 
previous  question,  that  is,  to  call  the  assumption 
which  lies  back  of  the  fallacy  into  question. 

Ignoratio  Elenchi,  according  to  Aristotle,  is  a 
fallacy  which  arises  from  "ignorance  of  the  nature 
of  refutation."  In  order  to  refute  an  assertion, 
Aristotle  says  we  must  prove  its  contradictory;  the 
proof,  consequently,  of  a  proposition  which  stood  in 
any  other  relation  than  that  to  the  original,  would 
be  an  ignoratio  elenchi. 

Since  Aristotle,  the  scope  of  the  fallacy  has  been 
extended  to  include  all  cases  of  proving  the  wrong 


574  A  TEXT-BOOK  OF  LOGIC 

point.  Thus,  when  H.  Spencer,  in  arguing  against 
the  advocates  of  a  classical  education,  says  that 
"Throughout  his  after  career,  a  boy,  in  nine  cases 
out  of  ten,  applies  his  Latin  and  Greek  to  no  prac- 
tical purposes,"  he  is  guilty  of  an  ignoratio  elenchi, 
for  the  argument,  as  Welton  points  out,  "ignores 
the  fact  that  the  advocates  of  a  classical  education 
do  not  claim  that  Latin  and  Greek  are  of  direct  use 
in  practical  life.  What  they  do  urge  is  that  the 
study  of  the  classics  furnishes  an  unrivalled  mental 
training;  and  it  is  this  proposition  which  a  true 
cAcyxo?  (elenchus)  must  disprove."  With  this  inter- 
pretation of  the  fallacy  Whately  is  in  agreement. 
He  writes :  "I  am  required  to  prove  a  certain  con- 
clusion ;  I  prove,  not  that,  but  one  which  is  likely  to 
be  mistaken  for  it;  in  that  lies  the  fallacy.  .  .  For 
instance,  instead  of  proving  that  'this  person  has 
committed  an  atrocious  fraud/  you  prove  that  'this 
fraud  he  is  accused  of  is  atrocious /  instead  of  prov- 
ing, as  in  the  well-known  tale  of  Cyrus  and  the  two 
coats,  that  'the  taller  boy  had  a  right  to  force  the 
other  boy  to  exchange  coats  with  him/  you  prove 
that  'the  exchange  would  have  been  advantag- 
eous to  both/  instead  of  proving  that  'a  man 
has  not  a  right  to  educate  his  children  or  dis- 
pose of  his  property  in  the  way  he  thinks  best/  you 
prove  that  'the  way  in  which  he  educates  his  chil- 
dren or  disposes  of  his  property  is  not  really  the 
best;'  instead  of  proving  that  'the  poor  ought  to  be 
relieved  in  this  way/  you  prove  that  'they  ought  to 
be  relieved.'  "  The  fallacy  usually  occurs,  as  Jevons 


FALLACIES  575 

remarks,  "in  the  course  of  long  harangues,  when 
the  multitude  of  words  and  figures  leaves  room  for 
confusion  and  forgetfulness."  Hence,  an  ignoratio 
elenchi  has  been  called  by  Aikins  the  fallacy  of  the 
forgotten  issue.  Thus  it  is  frequently  necessary, 
for  example  in  debate,  to  call  the  discussion  back  to 
the  point  at  issue.  For  example,  in  a  speech  in  the 
House  of  Commons,  Canning  is  reported  to  have 
said,  in  reply  to  Mr.  Percival,  that  "The  question  is 
not,  as  assumed  by  my  opponent,  whether  we  shall 
continue  the  war  in  the  Peninsula,  but  whether  it  is 
essential  to  our  success  in  the  war  that  our  present 
system  of  currency  remain  unchanged." 

The  nature  of  the  fallacy,  then,  consists  in  sub- 
stituting for  a  certain  issue  another  which  is  more 
or  less  closely  related  to  it,  and  arguing  the  substi- 
tuted issue.  The  fallacy  does  not  take  into  account 
whether  the  arguments  do  or  do  not  really  support 
the  substituted  issue,  it  only  calls  attention  to  the 
fact  that  they  do  not  constitute  a  proof  of  the  orig- 
inal one.  Sudents  are  quite  often  guilty  of  an 
ignoratio  elenchi  when  in  reply  to  questions  they 
substitute  some  other  though  related  question  and 
allow  their  answers  to  be  guided  by  it.  It  is  a  par- 
ticularly prevalent  and  subtle  fallacy  and  it  assumes 
a  great  variety  of  forms.  But  whenever  it  occurs 
and  whatever  form  it  takes,  it  is  brought  about  by 
an  assumption  that  leads  the  person  guilty  of  it  to 
substitute  for  a  definite  subject  of  inquiry  another 
which  is  in  close  relation  with  it.  In  the  petitio 
principii  the  fallacy  may  be  described  as  an  assump- 


576  A  TEXT-BOOK  OF  LOGIC 

tion  of  the  premises ;  in  the  complex  question,  as  an 
assumption  of  the  answer;  and  in  the  ignoratio 
elenchi,  as  an  assumption  of  the  question  at  issue. 

Whenever,  for  any  reason,  a  conclusion  does  not 
follow  from  the  assigned  premises,  we  have,  in  the 
literal  sense  of  the  term,  a  Non  Sequitur.  When 
used  in  this  sense  to  include  all  the  errors  in  reason- 
ing which  leads  to  erroneous  conclusions,  the  term 
is  generic,  and  must  be  understood  as  synonymous 
with  'fallacy.'  Any  kind  of  loose  or  inconsequential 
argument,  from  this  point  of  view,  would  be  a  non 
sequitur. 

More  particularly  considered,  the  fallacy  of  non 
sequitur,  as  was  indicated  by  Aristotle,  is  the  name 
we  apply  to  the  erroneous  conclusion  of  a  hypo- 
thetical syllogism.  Aristotle  regarded  it  as  an 
"argument  from  the  affirmation  of  the  consequent," 
and  for  this  reason  it  is  sometimes  called  the  fallacy 
of  the  consequent.  If,  for  example,  we  argue  that 
a  particular  individual  who  has  no  visible  means  of 
support  must  be  a  prefessional  thief,  because  "if 
a  man  is  a  professional  thief,  he  will  have  no  visible 
means  of  support,"  the  argument  will  be  fallacious 
because,  as  we  have  seen,  no  conclusion  can  be 
reached  by  affirming  the  consequent  of  hypothetical 
propositions.  The  term  non  sequitur  may  also  be 
applied  to  the  other  hypothetical  fallacy  of  denying 
the  antecedent.  In  both  the  cases  to  which  the  term 
has  been  said  to  apply,  the  assumption  is  made  that 
the  relation  between  antecedent  and  consequent  of 
the  major  premise  is  causal,  an  assumption  which 


FALLACIES  577 

we  have  no  right  to  make  in  view  of  the  complex 
interconnection  of  the  facts  with  which  our  human 
knowledge  has  always  to  deal.  But  if  it  is  made, 
the  only  way  we  can  avoid  a  possible  fallacy  is  to 
call  into  question  the  assumption,  and  thereby  to 
raise  definitely  the  question  whether  antecedent  and 
consequent  are  causally  connected  or  not. 

The  attempt  has  sometimes  been  made  to  apply 
the  name  non  sequitur  to  the  fallacies  which  occur 
in  connection  with  categorical  arguments.  This 
cannot  be  considered  a  useful  employment  of  the 
term.  For  if  the  term  applies  to  any  and  all  of 
these  errors,  it  must  be  regarded,  as  we  have  said 
above,  as  a  generic  term,  and  loses  all  particular 
significance,  and  if  it  is  used  of  a  particular  kind 
of  categorical  fallacy,  it  immediately  takes  its  place 
as  a  synonym  of  the  name  of  that  fallacy.  Some 
logicians,  however,  do  not  take  this  view  of  the  case, 
and  they  assign  the  term  to  a  group  of  cate- 
gorical arguments  of  which  the  following  may 
be  said  to  be  fairly  representative :  'Episcopacy  is 
of  scriptural  origin,  the  Church  of  England  is  the 
only  established  church  in  England,  therefore  the 
church  established  in  England  is  the  only  church 
that  should  be  supported.'  Again,  'Pennsylvania 
contains  rich  coal  and  iron  mines,  Pennsylvania  has 
no  sea  coast,  therefore  the  battle  of  Gettysburg  was 
fought  in  that  state/  These  examples  are  so  flimsy, 
as  examples  of  argument,  that  the  only  sensible 
course  to  take  with  regard  to  the  class  of  reasoning 

37 


578  A  TEXT-BOOK  OF  LOGIC 

for  which  they  stand  is  to  deny  that  it  can  have  any 
logical  recognition  at  all.  Logic  presupposes  at  the 
least  some  development  of  common  sense  on  the 
part  of  those  to  whom  it  addresses  itself,  and  one 
can  hardly  be  expected  to  take  so  low  an  estimate  of 
logic  as  to  think  that  it  can  be  of  any  possible  service 
to  the  individual  upon  whom  such  so-called  argu- 
ments would  have  the  least  chance  to  impose.  The 
logician  has  absolutely  nothing  to  do  with  such  an 
individual  who,  in  the  interests  of  society,  had  much 
better  be  placed  in  the  care  of  an  alienist. 

We  conclude,  therefore,  that  non  sequitur  is  a 
name  that  can  be  applied  only  to  fallacies  of  the  kind 
that  occur  in  the  course  of  hypothetical  arguments. 
The  fallacy  consists  in  misinterpreting  the  implica- 
tions of  the  relation  of  antecedent  and  consequent 
stated  in  the  major  premise  of  hypothetical  syllo- 
gisms. 

Fallacies  of  Interest.  Knowledge,  as  we  have 
shown,  depends  for  one  of  its  conditions  upon  what 
we  call  interest.  But  knowledge  is  not  secured  and 
advanced  by  any  or  any  kind  of  interest.  It  is  only 
when,  as  we  have  seen,  the  interest  is  directed 
toward,  and  is  accompanied  by  a  desire  to  ascertain, 
the  nature  and  relations  of  the  objects  by  which  it 
is  stimulated  that  it  can  be  considered  to  be  of 
service  in  the  establishment  of  knowledge  in  the 
strict  sense  of  that  term.  The  interest  that  must  be 
recognised  as  an  indispensable  condition  of  all 
knowledge  whatever  is  specifically  an  interest  that 
points  toward  and  terminates  in  the  establishment 


FALLACIES  579 

of  the  knowledge  relation.  Whenever  any  other 
interest  than  this  is  allowed,  consciously  or  uncon- 
sciously, to  influence  the  steps  we  take  toward 
knowledge,  or  the  conclusions  we  accept,  the  process 
and  the  conclusion  are  for  that  reason  fallacious. 
Instances  of  the  kind  of  argument  just  indicated 
will  be  considered  in  the  following  paragraphs,  and 
they  are  grouped  together  because  they  all  imply 
that  some  other  interest  has  been  substituted  for 
the  one  which  alone,  as  we  have  said,  can  be  of 
service  in  the  attainment  of  truth. 

Perhaps  the  most  reputable  of  the  fallacies  of 
the  kind  in  question  is  that  which  is  known  as  post 
hoc,  ergo  propter  hoc.  In  discussing  the  problems 
connected  with  the  establishment  of  causal  relations, 
we  have  seen  that  a  succession  of  events  is  to  be 
interpreted  always  as  containing  the  suggestion  of 
a  possible  causal  connection  between  the  events  in 
question,  or  with  other  with  which  they  are  con- 
stantly associated ;  but  we  saw  also  that  the  succes- 
sion itself  is  never  to  be  taken  as  evidence  of  such 
connection.  If,  therefore,  neglecting  this  latter  con- 
sideration, we  should  argue  from  an  observed  suc- 
cession of  events  to  the  causal  connection  of  the 
events,  the  conclusion  would  be  fallacious  because 
the  only  reason  that  could  be  assigned  for  the  infer- 
ence, namely,  that,  since  the  one  event  had  followed 
the  other,  it  was,  therefore,  caused  by  that  other, 
is  never  sufficient  to  establish  a  causal  relation.  The 
fallacy  arises,  then,  from  neglect  of  the  negative 
criterion  of  causal  relations  to  which  we  have  just 


580  A  TEXT-BOOK  OF  LOGIC 

referred,  namely,  that  mere  succession  is  never  a 
sufficient  reason  for  a  causal  inference. 

The  relative  prevalence  •  of  this  fallacy,  and  the 
charitable  attitude  most  of  us  take  toward  those  who 
are  guilty  of  it,  suggest  that  the  error  which  it 
implies  lies  somewhat  deeper  in  the  mental  life  than 
some  others  that  have  come  before  us.  If  this  is 
true,  the  explanation  and  full  exposition  of  the 
nature  of  the  fallacy  belong  to  psychology  rather 
than  to  logic.  In  a  general  way,  however,  we  can 
see  that  whenever  the  scientific  interest,  which  seeks 
to  safeguard  conclusions  from  possible  sources  of 
error,  is  not  strictly  emphasised,  or  when  it  is  for 
some  reason  temporarily  weakened,  it  is  easy  for  the 
human  mind  to  slip  into  one  of  the  more  usual  or 
conventional  attitudes  toward  the  objects  of  its  ex- 
perience, and  thus  to  arrive  at  conclusions  which, 
to  the  extent  that  this  has  taken  place,  are  fallacious. 
In  these  fallacies,  we  observe  a  tendency  to  confuse 
associative  combinations  with  causal  connections,  a 
tendency  which  is  emphasised  whenever  the  prac- 
tical takes  the  place  of  the  theoretical  interest  in 
determining  our  relations  to  the  objects  of  our  ex- 
perience. An  example  of  this  fallacy,  frequently 
met  with  in  educational  circles,  is  the  contention 
that  because  students  who  are  handicapped  by  the 
necessity  of  earning  their  livelihood  usually  manage 
to  pass  their  examinations,  while  others  who  are 
not  so  handicapped  sometimes  fail,  the  handicap  is 
part  of  the  cause  of  their  success.  In  similar 
fashion,  we  have  heard  it  argued  that  because  Spur- 


FALLACIES  581 

geon,  who  never  went  to  college,  was  a  great 
preacher,  that  this  was  due  to  the  fact  that  he  never 
attended  college.  There  is  more  common  sense  and 
logic  in  Spurgeon's  remark,  referring  to  the  above 
contention,  that  the  result  was  accomplished  in 
spite  of  his  lacking  a  collegiate  training. 

There  are  a  number  of  fallacies  which  are  due 
still  more  obviously  to  the  way  in  which  arguments 
connect  themselves  with  interests  which  are  distinct 
from  the  one  with  which  our  search  for  truth  is 
more  particularly  associated,  and  in  which  the  con- 
clusion assumes  a  character  in  conformity  with 
these  interests.  When,  for  instance,  an  argument 
makes  an  appeal  to  the  character,  principles,  pro- 
fession, or  interests  of  an  individual,  and  it  is  ac- 
cepted or  rejected  for  that  reason,  there  results  a 
fallacy  which  is  called  an  argumentum  ad  hominem. 
If,  for  example,  the  evidence  for  the  movement  of 
the  earth  round  the  sun  is  rejected  because  it  is 
inconsistent  with  one's  religious  convictions,  the 
rejection  is  fallacious  because  the  argument  reaches 
its  conclusion  by  the  substitution  of  the  religious 
for  the  scientific  interest.  If,  again,  the  fact  that 
one  owns  stock  in  a  brewery  is  allowed  to  influence 
his  judgment  as  to  what  conclusion,  with  respect  to 
the  sale  of  alcoholic  beverages,  is  warranted  by  the 
scientific  evidence  that  is  available  on  the  physio- 
logical effects  of  alcohol  on  the  human  system,  he  is 
guilty  of  the  fallacy  under  consideration.  When, 
once  more,  the  demands  of  religion  upon  the  indi- 
vidual are  rejected  because  preachers  or  church 


582  A  TEXT-BOOK  OF  LOGIC 

members  are  not  free  from  obvious  faults,  or  when 
they  are  accepted  because  thereby  business  will  be 
helped,  the  position  in  each  case  involves  an  ad 
hominem  fallacy. 

The  admission,  by  courts  of  law,  of  testimony 
bearing  upon  the  character  of  witnesses,  requires 
a  word  of  explanation,  because  it  seems  to  be  in 
contravention  of  the  recognised  fallacious  nature 
of  the  arguments  we  are  now  considering.  The 
difficulty  created  by  this  instance  is  removed  when 
we  observe  that  courts  of  law  do  not  admit  testi- 
mony as  to  the  character  of  witnesses  for  the  pur- 
pose of  deciding  whether  the  verdict  shall  be  for 
or  against  the  plaintiff,  but  for  the  purpose  of 
eliminating,  from  the  evidence  that  comes  before  it, 
testimony  that  is  irrelevant  to  the  issue,  that  is, 
testimony  which,  because  it  is  prejudicially  affected 
by  the  character  of  the  individual  who  gives  it, 
involves  an  argumentum  ad  hominem.  Prejudiced 
or  perjured  evidence  is  fallacious  in  exactly  the 
sense  in  which  any  ad  hominem  argument  is  falla- 
cious. 

When  an  argument  is  accepted  because  it  enlists 
on  one  side  or  other  of  the  question  at  issue,  our 
feelings,  passions  or  prejudices,  it  is  called  an  argu- 
mentum ad  populum.  This  is  essentially  the  fallacy 
of  public  address.  Any  cause,  as  we  all  know,  that 
can  bring  impressive  oratory  and  brilliant  metaphor 
to  its  aid  is  very  likely  to  secure  the  support  of  many 
upon  whom  the  cause  itself  and  the  arguments  which 
really  support  it,  would  have  little  or  no  influence. 


FALLACIES  583 

Conspicuous  examples  of  fallacious  reasoning  of 
this  kind  may  be  found  on  almost  every  page  of  the 
voluminous  writings  of  the  late  Robert  Ingersoll. 
A  somewhat  similar  fallacy  is  that  which  is  known 
as  argumentum  ad  misericordiam.  In  this  case,  our 
judgment  is  determined  by  the  appeal  that  is  made 
to  our  pity  or  sympathy.  Whenever,  for  example, 
we  recommend  a  cause  by  emphasising  the  plight  of 
those  whom  it  is  intended  to  benefit,  or  give  our  sup- 
port because  of  our  interest  in  the  individuals  who 
advocate  it,  or  give  alms  to  a  beggar  because  he  is 
in  rags,  we  are  guilty  of  letting  our  sympathy  inter- 
fere with  our  judgment,  and  this  is  exactly  what 
occurs  in  any  argumentum  ad  misericordiam. 

The  influence  of  a  great  name  or  of  long  estab- 
lished customs  is  pretty  generally  recognised  as  serv- 
ing a  useful  purpose  in  the  development  of  the  indi- 
vidual and  the  race.  When,  however,  our  reverence 
for  individuals  or  institutions  leads  us  to  accept, 
without  consideration  of  the  arguments  which  may 
be  advanced  for  and  against  them,  positions  which 
receive  the  support  of  or  are  in  conformity  with 
any  established  authority,  we  are  said  to  be  guilty 
of  the  fallacy,  argumentum  ad  verecundiam.  This 
is  a  fallacy  to  which  the  conservatives  among  us 
are  particularly  prone.  Our  interest  in  order,  in 
things  as  they  are,  unless  balanced  by  a  due  regard 
for  change,  may  lead  us  to  accept  a  position  merely 
because  it  is  in  agreement  with  some  established 
custom,  or  to  reject  another  merely  because  it  re- 
quires the  rejection  of  some  accepted  authority.  A 


584  A  TEXT-BOOK  OF  LOGIC 

peculiarly  aggravated  form  of  the  fallacy  comes  to 
light  in  those  instances  where  an  individual's  right 
to  speak  with  authority  in  one  field  of  knowledge  is 
taken  as  the  ground  of  our  acceptance  of  that  indi- 
vidual's opinion  in  another  field  with  respect  to 
which  he  has  no  special  acquaintance.  "The  pres- 
tige of  a  great  name,"  as  Creighton  remarks,  "is 
thus  irrelevantly  invoked  when  no  significance  prop- 
erly belongs  to  it.  Thus,  for  example,  a  successful 
general  is  sometimes  supposed  to  speak  with  author- 
ity upon  problems  of  statescraft,  and  the  opinions 
of  prominent  clergymen  are  quoted  regarding  the 
latest  scientific  or  political  theories." 

REFERENCES 

H.  A.  Aikins,  The  Principles  of  Logic,  Chs.  XVIII.,  XIX.,  XX. 
J.  E.  Creighton,  An  Introductory  Logic,  3d  Edition,  Chs. 

XII.,  XX. 
J.  G.  Hibben,  Logic,  Deductive  and  Inductive,  Part  I.,  Ch. 

XIX.,  Part  II.,  Ch.  XVI. 
W.   S.  Jevons,  Elementary  Lessons  in   Logic,  Lessons  XX., 

XXI. 
S.  '  H.    Mellone,    An    Introductory    Text-Book    of    Logic,    3d 

Edition,  Ch.  X. 
C.   Read,   Logic,  Deductive   and   Inductive,   3d   Edition,   Ch. 

XXIV. 
W.  J.  Taylor,  Elementary  Logic,  Ch.  XVIII. 

ADVANCED 

W.  R.  B.  Gibson,  The  Problem  of  Logic,  Ch.  XXVIII. 
H.  W.  B.  Joseph,  An  Introduction  to  Logic,  Ch.  XXVII. 
J.  S.  Mill,  A  System  of  Logic.  Book  V. 
F.  C.  S.  Schiller,  Formal  Logic,  Ch.  XXIII. 


FALLACIES  585 

A.  Sidgwick,  Fallacies. 

J.  Welton,  A  Manual  of  Logic,  Vol.  II.,  Book  VII. 

QUESTIONS 

1.  What  is   an   inductive   fallacy,   and   into   what   classes 
may  such  fallacies  be  divided. 

2.  What  testimony  can  you  quote  showing  the  importance 
of  a  careful  and  accurate  use  of  language  for  logical 
thinking? 

3.  What  did  Bacon  mean  by  Idols  of  the  Market  Place? 

4.  How  does  Locke  explain  the  fact  that  language  often 
renders  thought  fallacious? 

5.  In   what   two  ways   may  the   observation   of   facts   be 
fallacious? 

6.  State  and  illustrate  the  fallacy  of  insufficient  observa- 
tion. 

7.  What  do  you  understand  by  a  negative  instance? 

8.  What  is  the  testimony  of  Bacon  and  Darwin  as  to  the 
importance  of  negative  instances? 

9.  In  what  respect  does  education  predispose  one  to  the 
neglect  of  negative  instances? 

10.  What  does  Bacon  mean  by  Idols  of  the  Theatre? 

11.  In   what   form   is   the   fallacy   described   by   Bacon   in 
these  terms  likely  to  appear  at  the  present  day? 

12.  What  is  the  fallacy  of  incomplete  or  imperfect  obser- 
vation? 

13.  Explain  how  the  personal  factor  may  lead  to  incomplete 
or  imperfect  observation. 

14.  In  what  way  does  technique  affect  the  thoroughness  of 
observation? 

15.  What  are  the  two  fallacies  of  explanation  considered 
in  the  text? 

16.  Explain  what  is  meant  by  a  hasty  generalisation. 

17.  To  what  consideration  of  scientific  importance  does  the 
possibility  of  hasty  generalisations  point? 

18.  What  is  the  fallacy  of  false  analogy? 


586  A  TEXT-BOOK  OF  LOGIC 

19.  In  what  respect  is  the  fallacy  of  false  analogy  similar 
to  the  fallacy  of  figurative  language? 

20.  In  what  respect  does  false  analogy  resemble  the  fallacy 
of  negative  instances? 

21.  What  is  the  general  character  of  the  fallacies  of  the 
context? 

22.  Into  what  two  classes  may  fallacies  of  the  context  be 
divided?     Describe   each   class,   naming  the  particular 
fallacies  that  belong  therein. 

23.  What  do  we  mean  by  a  fallacy  of  assumption? 

24.  Describe  the  essential  character  of  a  petitio  principii. 

25.  How  may  we  proceed  to  break  down  a  petitio  principii? 

26.  How   may   a   verepov   irporepov  be   distinguished   from   a 
circulus  in  probando,  and  how  are  they  related   to   a 
petitio  principii? 

27.  What  is  the  fallacy  of  the  complex  question? 

28.  What,  according  to  Aristotle,  is  an  ignoratio  elenchi? 

29.  What  is  an  ignoratio  elenchi  according  to  modern  logic? 

30.  What  is  Aikin's  term  for  an  ignoratio  elenchi,  and  dis- 
cuss its  appropriateness. 

31.  From  the  standpoint  of  the  assumptions  involved,  how 
do  the  petitio  principii,  the  complex  question,  and  the 
ignoratio  elenchi  differ  from  one  another? 

32.  What  is  the  genereic  meaning  of  the  non  sequitur? 

33.  What,   according  to   Aristotle,   is   a   non  sequitur,   and 
what,  accordingly,  is  another  name  for  the  fallacy? 

34.  With  what  meaning  is  the  term  non  sequitur  now  used 
in  modern  logic? 

35.  Discuss  the  relation  of  the  non  sequitur  to  categorical 
arguments. 

S6.     What  are  the  fallacies  of  interest? 

37.  Describe  the  post  hoc,  ergo  propter  hoc  fallacy. 

38.  What  is  understood  by  an  argumentum  ad  hominem? 

39.  Does  the  admission  of  evidence  as  to  the  character  of 
accused  persons,  or  of  those  giving  evidence,  by  courts 
of  law  involve  the  verdict  in  the  ad  hominem  fallacy? 
Explain. 


FALLACIES  587 

40.  What  is  the  argumentum  ad  populum?     Illustrate. 

41.  State  and  illustrate  the  argumentum  ad  misericordiam. 

42.  Show  by  means  of  illustrations  the  nature  of  the  argu- 
mentum ad  verecundiam. 

EXERCISES 

Examine  the  following  arguments,  and  state  in  what  re- 
spects, if  any,  they  are  fallacious,  the  technical  name  of 
the  fallacy  of  which  each  is  guilty,  and  the  class  to 
which  the  fallacy  belongc: 

(1)  In  the  act  of  landing  on  the  African  coast,  Caesar 
accidentally  stumbled,  and,  as   he   did   so,   he  ex- 
claimed, 'Africa!    I  embrace  thee.'     Against  what 
fallacy  on  the  part  of  his  followers  was  this  ex- 
clamation intended  to  guard? 

(2)  It  is   a  dictum  of  the   Cartesian   philosophy  that 
whatever  can  be  clearly  conceived  exists.     Is  this 
fallacious,  and  if  so,  why? 

(3)  The  opponents   of  the   Copernican   system   argued 
that  if  the  earth  moved,  a  stone  let  fall  from  the 
top  of  a  tower  would  not  reach  the  ground  at  the 
foot  of  the  tower,  but  at  a  point  some  distance 
from    it,    in    a    direction    opposite   to    the    earth's 
movement.     Such,  however,  is  not  the  fact. 

(4)  It  is  reported  by  travelers  that  the  negroes  among 
whom  coral  is  worn  as  an  amulet  affirm  that  it  is 
always    affected    by    the    state    of    health    of    the 
wearer,    becoming   pale   in    disease.      This    is    not 
true. 

(5)  Women,    as    a    class,    are    supposed    not    to    have 
hitherto  been  equal  in  intellect  to  men,  therefore 
they  are  necessarily  inferior. 

(6)  The  twenty-five  years   of   Republican  tariff  legis- 
lation have  been  a  nera  of  unparallelled  prosperity. 
Why  kill  the  goose  that  lays  the  golden  egg? 


588  A  TEXT-BOOK  OF  LOGIC 

(7)  The  metropolis  of  a  country  may  be  compared  to 
the  heart  of  a  living  body,  hence  we  may  infer  that 
any  considerable  increase  in  size  of  the  metropolis 
is   evidence  of   a   diseased   condition   of  the   body 
politic. 

(8)  The   early   Teutonic   societies   were   held    together 
by  ties  of  kinship,  because  all  societies  were  so 
held  together  originally. 

(9)  It  is  sometimes  contended  that  because  punishment 
can  only  intimidate  it  is  brutalising,  and  therefore, 
it  should  not  be  employed,  but  that  only  shows  that 
there  are  persons  who  are  so  brutalised  that  they 
can  be  influenced  only  through  fear. 

(10)  The  apologists  of  Charles  I.,  McCaulay  complains, 
defend   the  king  by  urging  that  he  was   a   good 
judge  of  pictures  and  indulgent  to  his  wife. 

(11)  This  is  a  party  measure  and  therefore  we  must 
vote  for  it. 

(12)  A  religion  which  elevates  the  soul  above  the  body 
can  survive  persecution,   and   since  the  Christian 
religion   has    survived   persecution,   it   enables   its 
devotees   to   prefer   the   interests    of   the    soul   to 
those  of  the  body. 

(13)  It  is  frequently  assumed,  because  the  animals  and 
men    native    to    countries    of    inclement    climates, 
where  the  conditions  of  life  are  severe,  are  usually 
robust,    that    the    hardships    they    are    forced    to 
undergo  in  youth  are  the  cause  of  their  hardiness. 

(14)  I  do  not  know  that  you  will  approve  it,  but  I  gave 
him  a  pair  of  shoes,  an  old  coat,  and  something 
to  eat.     I  felt  so  sorry  for  him. 


INDEX 


Abelard,   on  universals,  93 
Accent,  fallacy  of,  5l7f 
Accident,  as  predicable,  186 

converse  fallacy  of,  521 
fallacy  of,  620f 

Acquipollence,  education  by,  279f 
Affirming  the   consequent,    fallacy    of, 

540f 
Agreement,  Method  of,  477f 

a   method   of  observation, 

480,  482 

elimination  and,  478 
Jevon's  formulation  of,  477 
Kmits  of,  480f 
Mellone's   formulation   of, 

479 

method  of  single.  477 
method   of  double,   490 
Mill's  formulation  of,  477 
states  an  ideal,  479f 
Agreement  and  Difference,  Method  of, 

486f 

application    of,    490f 
conditions  of  its  use,  486f, 

496 

field  of  application,  487 
Melone's    formulation    of, 

489 

Mill's  formulation   of,   488 
Aikins,  on  the  forgotten  issue,  575 
Ambiguity,     as     fundamental     logical 

problem,  164 
criticism      of     traditional 

view    of,    163f 
fallacy  and,  614 
judgment  and,  54 
structural,    522f 


traditional  view  of,  162f 
translation  and,  165f 
verbal,  515f 

of  terms,  fallacies  of,  534f 
Ambiguous     disjunction,     fallacy     of, 

547f 

Amphibole,    fallacy    of,    522f 
Analogy,  conditions  of,  413f,  41"f 
false,  fallacy  of,  565f 
function     of,     in     induction, 

416f 

limits   of,  412f,  418 
logical     character     of,     411f, 

419f 

meaning  of,  409f 
translation  and,  165f 
Anselm,  on  universals,  93 
Aquinas,   on  universals,   93 
Arguments,    basis    of    categorical,    297f 
categorical,  297f,  SOlf,  326f 
circular,  572 
constructive    hypothetical, 

361f 

deductive,   532 
destructive      hypothetical, 

353f 

dilemmatic,  354f 
disjunctive,    343f,    644f 
hypothetical,    348f,    539f 
inductive,    532 
logical    problem    of    cate- 
gorical, 298 

mixed  disjunctive,  343f 
simple  disjunctive,  343f 
validity  of  disjunctive, 

345f 

Argumentum,  a  dicto  secundum  quid, 
521 


589 


590 


INDEX 


a  dicto  simpliciter,  520 
ad  hominem,  581 
ad  misericordiam,   583 
ad  populum,  582f 
ad  verecundiam,  583f 
Aristotle,  list  of  Predicables,  181 
on  analogy,  409 
on   fallacies,  508 
on  ignoratio  Elenchi,  573 
on   logic,   12,   18 
on  non  seguitur,  576 
on  the  categories,  369 
on  the  classification  of  fal- 

lacies, 511 
on   the   fallacy   of   division, 

519 

on  what  can  be  defined,  182 
Assertion,  conditions   of   relevant,  36f 
grounded,  302 
grounds  of,  302 
judgment  as,  28f 
relevant,   36f 
truth  and,  58 
Assumption,  fallacies  of,  669f 


B 

/ 

Bacon,  on  Idols  of  the  Market  Place, 

653f 

on  Idols  of  the  Theatre,  559f 
on  imperfect  induction,  375 
on  negative  instances,  375,  567f 
on  perfect  induction,  374 
on  the  interrogation  of  nature, 

442 
the  herald  of  modern  learning, 

471 

Bosanquet,   on   negative   terms,   152 
Bradley,  on  disjunction,  342 

on  the   real  subject  of  judg- 

ment, 55 
on  the  'that'   and  the  'what* 

of  judgment,   49 
Brodie,    on   scientific  imagination,   424 


Categories,   defined,   369 

predication   and,   369 
Causation,   analysis  and,  455f 

complex    characts,    of    facts 

of,  449f 
elimination  as  a  method  of, 

474f 
hypothetical  statements  and, 

462f 

metaphysics  of,  458f 
Mill's  Methods  and,  473f 
necessity  and,  457f 
practical  aspect  of,  436f 
problem   of,  435f,  442f,  451  { 
purpose   and,  4.55 
reciprocal,  461,  473f 
relation     of     practical     and 
theoretical       aspects       of, 
440f 

relation   of   purpose  to,   449 
temporal  sequence  and,  445f 
theoretical  aspect  of,  438f 
Cause,   analysis,   4i55f 

certainty  and,  455 

complex     character     of,     449f, 

453f 

conditions  and,   451 
effect  and,   447f,  453f 
indeterminateness   of,   452 
necessity    of,   456f 
occasion  and,  461 
probability  and,  464f 
purpose   and,   449,   455 
reciprocity  of  effect  and,  461f 
temporal   antecedence   and,  445f 
Causes,  composition    of,    499 

criticism   of  plurality  of,  466f 
permanent,  486 
plurality  of,  461f,  542f 
Classification,  artificial,   215 

comparison     and,     212f, 

377 

conditions  of,  214f 
defined,  ffllf 
definition  and,  212f 


INDEX 


591 


division  and,  213f 
induction  and,  216 
kinds  of,  2l5f 
Mill's   doctrine  of,  criti- 
cised, 216 
natural,   215 
practical,  2l7f 
purpose  and,  214,  216f 
scientific    and     popular, 

377f 
statistical   methods  and, 

ml 

theoretical,  217 
Colligation,  nature  of,  378f 

value  of,   380 

Comparison,    classification    and,    214 
definition  and,  169,  190 
relation  of  judgment  and 

reasoning  to,  303 

Complex  Question,  fallacy  of,  572f 
Composition,   converse   fallacy   of,   519 

fallacy  of,  518f 

Concept,  conceptualist  view  of,  93 
logical  view  of,  98f 
nominalist  view  of,  93 
psychological  view  of,  93 
realist  view   of,   92f 
Conclusion,  as  grounded  assertion,  302 

denned,   304 
Concomitant    Variations,    Method    of, 

486,  492f 
conditions     of     its    use, 

493,   494f,   497 
field    of   its   application, 

496 
Mill's     formulation     of, 

492 
quantitative    phenomena 

and,  494f 

the  principle  of,  493 
Conditions,  cause   and,  461 

essential,   456 

Context,     relation    of    judgment    and 
proposition  to,  54,  82,  87 


Contradiction,   basis  of,   211 
fallacy   of,   627 
meaning  of,  272f 
Contradictories,  meaning  of,  210 
Contraposition,  education  by,  288f 

table  of,  289 

Contrariety,   meaning  of,  266f 
Connotation,   meaning  of,   109f,   158 
of  collective  term,  128 
of  general  term,  125 
of  individual  term,  122f 
of  positive   term,   144f 
problems    of,    117,   158 
relation    to    denotation, 

llOf 

Conversion,   contrapositive,   288f 
fallacies  of,  530f 
meaning  of,  283f 
method  of,  284f 
per  accidens,  286 
rule  of,  285 
simple,  285f 
table   of,   288 
Copula,    as   "sign   of    predication",   94, 

234 

existential  views  of,  95f 
function  of,  91f,  234 
how   expressed,   91 
relational   view   of,  92f 
Creighton,    on    argumentum    ad    vere- 

cundiam,   684 
on  fallacy  of  accent,  618 
on  the  Joint  Method,  487f, 

491f 

on      the      connotation      of 
proper   names,   122 


Darwin,    on    theorising,    399 

on  negative  instances,  658 
Definition,    classification    and,    212f 

comparison    and,    109,    190, 

212f 

conditions  of,  I67f 
convertible    with    definien- 
dum,  179 


592 


INDEX 


dichotomy  and,  207f 
elementariness  of,  I79f 
genetic,   176 
homogeneity   of   terms    in, 

179 

indeterminateness  of,  196f 
negative,  180f 
per  genus  tt  differentiam, 

171f 

positive,  180 
problem  of,  159,  I80f 
real,  173f 
relation  of  division  to,  190, 

198f 
relation     of     purpose     to, 

I76f 

structural,  175 
synonyms  and,  180 
tests  of,  176f 
too  broad,  I77f 
too  narrow,  178 
verbal,  I73f 
when  employed,   167f,   170, 

190 

Denotation,  meaning  of,  108f,  114f 
of  collective  term,  128f 
of  general  term,  125 
of  individual  term,  122f 
of  positive  term,  144f 
problems  of,  117,  168 
relation     to      connotation, 

HOf 
Denying    the    antecedent,    fallacy    of, 

MM 

Designation,  as  concrete  term,  121 
meaning  of,  122f,  124 
Dichotomy,  definition  and,  207f 
division  by,  205f 
nature  of,  206f,  210 
value  of,  208f 
Difference,  Method  of,  482f 

a    method    of    experiment, 

482 

grounds  of  validity,  485f 
indirect  method  of,  490 
intermixture  of  effects  and, 
486 


Hellene's     formulation     of, 

484 

Mill's  formulation   of,   482 
single  method  of,  484 
Differentia,  as  predicable,  185f 

meaning  of,  172f 
Dilemma,    classes   of,  357f 

constructive,   357f 
denned,  355 
destructive,  8&8f 
nature  of,  354f 
structure  of,   356f 
validity  of,  359f 
Distributed,    meaning   of,    114f 

terms  in  categorical  prop- 
osition, 259f 

Disjunction,   basis  of,  340f 
exclusive,  341f 
exhaustive,  342f 
Division,   by    dichotomy,    205f 

classification   and,   213f 
conditions  of,  213f 
cross,  201 
fallacy   of,   519f 
logical,  exhaustive,  205 
meaning  of  logical,  191f,  198, 

196 

metaphysical,  194 
physical,   195 
principle  of,   195,   196f 
rules  of  logical,   192,   f,   200f 
terminology    of   logical,    199f 
verbal,  195 


Eductions,  by  aequipollence,  279f 
by  contraposition,  288f 
by  conversion,   288 
by  inversion,  290f 
by   negation,   288f 
by   obversion,   279f 
by   permutation,  279f 
classes  of,  279f 
fallacies    of,    529f 
meaning   of,   278f 


INDEX 


593 


schema  of,  292 
summary   of,  291 
table  of,  292 
Effect,  cause  and,  447f 

conditions  and,  461 

intermixture  of,  485f,  499 

nature  of,  452 

occasion  and,  461 

reciprocal    character    of    cause 

and,  461f 

temporal   sequence   and,   445f 
Enthymeme,  denned,  328 

elliptical  nature  of,  329 
Figure  of,  329 
Mood  of,  329 
Orders  of,   328 
syllogistic     character     of, 

328 

Enumeration,    generalisation   and   sim- 
ple, 386 
simple,    376f 

Episyllogism,  polysyllogism  and,  330 
Epicheirema,    nature    and    classes    of, 

335f 

Equivocation,  fallacy  of,  515f 
Error,  characteristic  of  assertion,  58 
compatibility    of    asserted    con- 
tent in,  68f 
conditions  of,  82,  97 
not  irrelevance,  66f 
purpose  and,  66 
Exclamations,  logic  of,  31f 
Experiment,  controlled  conditions,  403 
limitations  of,  401 
nature    of    scientific,    400, 

402f,  483f 

observation   and,  400 
relation    of     purpose    to, 

402f 
scientific  402f,   483 


Fact,   a  coexistent,  486 

colligation  and,  378f 
meanings  of,  367f 

•38 


relation   to  judgment,   368 

relations    of,    370f 

world  of,  37lf 
Fallacies,   categorical,   533 

classification   of,  511f 

deductive,    633f 

defined,   508f 

disjunctive,   544f 

hypothetical,  539f 

inductive,   552f 

a  dicto  secundum  quid,  521 

a  dicto  simpliciter,  520 

ad  hominem,  581 

ad  misericordiam,  583 

ad  populum,  582f 

ad  verecundiam,  583f 

categorical,   533 

classification  of,  511f 

deductive,  633f 

defined,    508f 

disjunctive,   644f 

hypothetical,    539f 

ignoratio  elenchi,  573 

inductive,  652f 

non  sequitur,  576f 

of  accent,  517f 

of  accident,  520f 

of  accident,  converse,  521f 

of     ambiguous     disjunction, 

547f 

of  amphibole,   522f 
of    assumption,   669f 
of  complex  question,  672f 
of   composition,   518f 
of  contrariety,  627f 
of  conversion,  530f 
of  division,  619f 
of  eduction,  529f 
of  education,  529f 
of  equivocation,  615f 
of  explanation,  563f 
of  false  analogy,  565f 
of  false  disjunction,  646 
of  false  parenthesis,  524 
of  four  terms,  534f 
of  hasty  generalisation,  663f 


594 


INDEX 


of     incomplete     disjunction, 
MM 

of  implication,  625f 

of  inference,  631f 

of  insufficient  premises,  637f 

of  interest,  578f 

of  interpretation,  614f 

of  language,  663f 

of  observation,  655f 

of  obversion,  529f 

of  opposition,  526f 

of  subalternation,  628f 

of  subcontraiety,  627f 

of  the  consequent,  676 

of  the  context,  667f 

petitio  principii,  670f 

post  hoc,  679f 

structural     ambiguity     and, 

522 
verbal  ambiguity  and,  615 


Generalisation,    causal    sequence    and 

empirical,  463f 
classification  and,  377f 
empirical,  376f,  385f 
hasty,  fallacy  of,  663f 
Mill  on,  376 
presuppositions  of,  377 
simple       enumeration 

and,  386 
statistical  methods 

and,  391f 
value      of      empirical, 

378,  385 

Genus,   meaning   of,   I72f 
as  predicable,  185f 

Gibson,    on   elimination   in    causal   in- 
quiries, 476f 

on   experimentation,  403 
on   statistical  method,  391 
Green,  on  colligation,  379 
Grote,   on   knowledge   of  acquaintance 
and  knowledge  about,  83 


H 

Hegel,  on  the  syllogism  of  analogy,  412 
Herschel,    his   contributions    to   induc- 
tive logic,  472 

on   residual   phenomena,   600 
Huxley,    on     intellectual     observation, 

400 
Hobbes,   on  language,  553 

on  the  scientific  imagination, 

425 
Hypothesis,  analysis  and,  421 

imagination  and,  426f 
limits  of,  420f 
living,  427 
nature  of,  420 
objections  to,  422f 
theory  and,  429f 
truth  and,  427 
verification   of,  427f 


Imagination,   science  and,424f 
Imperatives,  logic  of,  Slf 
Implication,   classes  of,  264f 
fallacies  of,   526f 
meaning  of,  263f,  278,  626f 
Induction,  analogy  and,  416f 

explanatory      methods      of, 

406f 

ground  of  truth  of,  387f 
hypothetical  statements  and, 

389 

imperfect,  373 
number    of    instances    and, 

386,  386f,  665 
perfect,   372,    376f 
problem  of,  366f,  372 
simple      enumeration      and, 

372f 

two  factors  of,  386f 
Inference,  by  private   conception,   279f 
fallacies  of,  531f 
immediate,   263f. 

Instances,  negative,  875,  484f,  556f 
positive,  484f 


INDEX 


595 


Intelligence,    nature   and   development 
of,  395f 

Interest,  assertion  and,   36f 

cansation   and,   449,  455 
classification  and,  214,  216f 
designation   and,  I23f 
error   and,   66 
experiment  and,  402f 
general  term  and,   125f 
judgment  and,  44f,  67,  117 
knowledge  and,  44f,  578f 
meaning  and,   117 
and  opinion,  464 
observation  and,  397,  402f. 

Interrogatives,   logic   of,   31f 

Inversion,  method  and  nature  of,  290 
obversion  and,  291 
tables  of,  291 

Irrelevance,  nature  and  forms  of,  65f 


James,  definition  of  conception,  26 

on  knowledge   of  acquaintance 

and  knowledge  about,  83. 
on      the      meaning      of      term 
thought,  25 
Jevons,  on  analogy,  419 

on  ignoratio  etenchi,  674f 
on  imperfect  induction,  374f 
on    the   antecedent    of    causal 

events,  450f 
on  the  dilemma,   359 
on  the  fallacy  of  accent,  517 
on  the  intermixture  of  effects, 

499 
on     the     Method     of     Single 

Agreement,  477 
on  the   occasion   of  an  event, 

in 

Joseph,    on    elimination    in    causal    in- 
quiries, 474f 

Judgment,  actual  subject  of,  52,  55 
ambiguity  of,  54f 
as  assertion,  28f,  29f,  36f 
as  grounded  assertion,  302 
belief  and,  97 


comparison  and,  303 
conditions  of,  36f 
content  of,   29,   82 
defined,  29,  50,  55 
difference  and,  240 
empirical,  general,  385f 
enumerative,    374 
error  and,  65f 
fact   and,   368 
fragmentariness  of,  83,  87 
groundless   statements   and, 

33f 

identity  and,  239 
incompleteness   of,  54 
interest  and,  44f,  67,  117 
limits  of,  67 
logical    subject    of,    52. 
mental     attitudes     akin     to, 

31f 
nature    of,   28f,   35f,    51,    55, 

303 

object  of,  47f,  50,  368 
objective  of,  50 
origin   of,   77f 
practical  aspect  of,  357 
presupposition  of,   52,  97 
probable,  62f 
proposition  and,  76f,  84,  94, 

303 
scientific,     and    probability, 

62f 

social,   and    probability,    62f 
subject-matter  of,  29,  47f 
theoretical    aspect    of,    35f, 

41f 

thought  and,  28f 
truth  of,  58f 

K 

Knowledge,    about,   83 

error  and,  65f 
interest  and,  44f,  578f 
meaning   of,   5f 
method  of,  logic  as,  20 
of  acquaintance,  83. 
opinion    and,   464 


596 


INDEX 


relation    of    syllogism    to, 

298f 

systematic,  6f,  391f 
truth  and,  58f ,  60f,  366 
.Knowledges,  logic  and  the,  9f,  18 
meaning  of,  9 
thought  and  the,  lOf 


Language,  Hobbes  on,  553 

judgment   and,   76,   84f,   96, 

98f 

Locke  on,  554f 
the  sciences  and,   160 

Locke,  on  language,  664f 

Logic,  as  an  art,  17f,  20f. 

as  method  of  thinking,  19 
as  science,   21f 
as  science  of  meaning,  20 
as  scientia  scientiarum,  llf 
as   scientific   method,   19 
Herschel's    contributions,   472 
humanistic  influence  in,  12f 
Mill's  historical  position  of,  472 
psychology  and,  14f,  20 
subject-matter   of,  If,  lOf 
the  knowledges  and,  9f 
the  sciences  and,  lOf 
thought  and,  lOf 

Lotze,  on  observation,  400 

M 

Major,  ambiguous,  fallacy  of,  534 

illicit  process  of,  536 
Marketplace,  idols  of,  553f 
Mathematical  proportion,  analogy  and 

400f 

syllogism  and,  300f 
Meaning,    absolute    and    relative,    dis 

tinction  between,  140f 
abstract,  130f 

abstract,     development     of 
134f 


abstract,    partial    views    of, 

131f 

collective,  126f 
concrete,  118,  ISOf 
concrete  and  abstract,  basis 
of      distinction     between, 
139 

contrary,    155 
disparate,  155 
general,    124f,   126 
incompatible,  238 
individual,  124f 
individual    concrete,    kinds 

of,  121f 

interest  and,  117 
negative,  143f,  236f 
negative,       conditions       of, 

145f 
negative    interpretation    of, 

149f,   154 

positive,  143,   2S5f 
privative,  143f,  236f 
Meinong,   on   object  and   objective   of 

judgment,    49f 
Mellone,    on   analogy,   416 

on   denying   the    antecedent, 

542 

on  induction,  416 
on  the  Joint  Method,  489 
on    the    Method    of    Agree- 
ment, 479 
on    the    Method    of    Differ 

ence,  484 
Methods,  experimental,  their  historical 

position,  47lf 
problem  to  which  they  apply, 

473f,  496 

statement  of,  477f 
Middle,   ambiguous,   fallacy   of,  534 

undistributed,  536 
Mill,   his    meaning    of    unconditional, 

459f 
historical  position   of  his  Logic, 

47lf 

on  analogy,  419 
on  a  philosophical  language,  553 


INDEX 


597 


on  causation,  444f 

on  colligation,  378f 

on  empirical  generalisation,  376 

on  hypothesis,  427 

on   imperfect  induction,   375 

on   invariable   sequence,  445f 

on  parity  of  reasoning,  381 

on  perfect  induction,  374 

on  permanent  causes,  486 

on  purpose  and  cause,  449 

on    the    complex    character    of 

causal  events,  449f,  457 
on    the    composition    of    causes, 

499 
on    the    connotation    of    proper 

names,  12f 
on  the  copula,  95f 
on    the   intermixture    of   effects, 

48Sf 

on  the  Joint  Method,  486f 
on     the     necessity     of     causal 

events,  456f 

on  the  plurality  of  causes,  461f 
on   the    relation    of   metaphysics 

to  causal  problems,  458f 
on    the    Method    of    Agreement 

477f 
on  the  Method  of  Concomitant 

Variations,  492f 
on    the    Method    of    Difference,. 

482f 

on  the  Method  of  Residues,  496f 
on  the   Methods  of  Experimen- 
tal inquiry,  47lf 

Minto,   on  Aristotelian  logic,  13,  21 
on   the  history  of  logic  ,471 

N 

Names,    connotation    of    proper,    112, 
121f 

denotation  of  proper,  121 

meaning  of,  88f 

terms  and,  88 
Necessity,  causal,  457f 


Negation,  bare,  152 

conditions  of,  145f 
double,  279 
eduction   by,  288f 
function  of,  238 
meaning  of,  149f,  153f,  238 
Non-ambiguity,  division  and,  190f 
fallacy  and,  515 
language  and,  160 
limits  of,  161f 

Nonsense,    logical    status    of,    238 
Non  sequitur,  fallacy  of,  576f 


Object,  affected  by  mode  of  apprehen- 
sion, 24f 
implication     of,     in     conscious 

process,  24f 
meaning  of,  24 
Observation,     analytic     character     of, 

398f 

development  of,  395f 
experimental,  400f,  453 
experimental,   limits   of, 

401 

imagination  and,  426 
limits  of,  556,  556f 
perceptual,   396f 
qualitative    methods    of, 

of,  399f 
scientific,   397f 
scientific     and     Method 

of  Residues,  500 
selective     character     of, 

399f 

theoretical,  401f,  453 
Obversion,  fallacy  of,  529f 
meaning  of,  279f 
method  of,  281f 
rules  of,  290 
table  of,  282 

Occasion,  meaning  of,  451 
Opposites,  contradictory,  210 
Opposition,  contradictory,  272f 
contrary,  266f 
fallacies  of,  526f 


598 


INDEX 


kinds  of,  266 
meaning  of,  265 
subaltern,  269f 
subcontrary,  273f 
square  of,  276f 
table  of,  279 
Optatives,  logic   of,  31f 


Pearson,  on  the  objectivity  of  science, 

423 

Permutation,    education    by,    279f 
Petitio  principii,   fallacy   of,  570f,  573 

575f 
Polysyllogism,  defined,  330 

progressive,  331 
prosyllogism  and,  330 
regressive,  331 
types  of,  33lf 
Post  hoc,  fallacy,  679f 
Porphyry,  list  of  Predicables,  181 

on   the   subject  of   predica 

tion,  182 
Tree  of,  210f 

Predicables,  Aristotle  on,  181f 
commensurate,  183 
lists  of,  181 
meaning  of,  181 
non-commensurate,       183 

185f 

Porphyry  on,  181f 
problem  of,  160,  181f 
Predication,  basis  of,  239 

categories  and,  369 

degrees  of,  222 

kinds  of  thing  and,  160 

181f 

meaning  of,  85f,  222 
Premises,  as  grounds  of  assertion,  302 
function  of,  305 
major  and  minor,  305 
negative,  fallacy  of,  537f 
particular,  fallacy  of,  537f 
propositions  as,  304f 


Probability,  causation   and,    464f 

characteristic  of  assertion, 

58 

conditions   of,   62f 
scientific    judgments    and, 

62,   64f 
Propositions,  affirmative,  235f,  238f 

affirmative  and  negative, 

relation  of,  238f 
^analysis  of,  84f 
apodeictic,  250f 
as  premises,  304 
assertoric,   247f 
categorical,  99,  102f 
categorical,    classification 

of,  222f 
categorical,     implications 

of,  255f 

causation    and    hypothet- 
ical, 462f 
compound,   244f 
compound     hypothetical, 

355f 

context  and,  82 
contraposition  of,  288f 
degrees   of   certainty    of, 

247 

distribution  and  the  cate- 
gorical,   259f 
disjunctive,  99,  lOOf 
eductive,   278f 
eductive,      fallacies      of, 

529f 

eductive,   schema  of,  292 
eductive,  table  of,  292 
exclusive,  241,  243f 
exceptive,   241  f 
exponible,  244 
hypothetical,    347f 
hypothetical,   and    causa- 
tion, 462f 
ideas  and,   77 
import    of,    79f 
indesignate,    232f 
induction  and  hypotheti- 
cal,   389 


INDEX 


599 


x  interpretation  of,  263f 
inversion   of,  290f 
judgment    and,    76f,    84, 

308 

kinds  of,  98f 
^meaning   of,    76,    85,    96, 

98f 

modality  of,  225,  246f 
negative,  236f 
opposed,  265f 
opposed,  fallacies  of,  526f 
opposed,  table  of,  279 
opposition  of,  265f 
origin  of,  78f 
particular,  230f 
problematic,  248f 
quality  of,  224f,  234f,  259f 
quality  and  quantity,  re- 
lation of,  255f 
quantity  of,  224,  225f,  259 
relations  of,  222f,  225 
simple    hypothetical,    99, 

lOlf 

singular,  228f 
statement— import  of,  79f, 

84 
structural    formulae    of, 

256f 

terms  and,  84f,  107 
the   sentence   and,   85 
truth— import   of,    79,    84 
types  of,  222f 
universal,  229f 
universal,   kinds   of,   230 
Proprium,  meaning  of,   184f 
Prosyllogism,  polysyllogism  and,  330 
Psychology,  definition  of,  26 
logic  and,  14f,  20 
of  thought,  25f,  35f 
Purpose,   see  Interest 
Pythagoras,    on   the   mathematical    in- 
terpretation of  nature,  393 


"C 

Quantity,    of    propositions,    224,    225f, 

269 
Quality,  of  propositions,  224f,  234f,  259f 


Reality,   belief  in,  97 

judgment  and,  52,  55 
meaning  of,  370f 
spheres  of,  97f 
Reasoning,   parity  of,  380f 
Residues,   Method   of,   496f 

intermixture  of  effects  and, 

498f 

Mill's  formulation  of,  498 
scientific    observation    and, 

600 

Roman  Church,  realism  of,  93 
Roscellinus,  on  universals,  93 


Schoolmen,  on  universals,  92 
Sciences,  aims  of  the,  406f,  423 

co-operation  in   the,   562f 
imagination  and  the,  424f 
language  and  the,  160 
method  of,  logic  as,  19 
nature   of  the,   21 
objectivity    of    the,    423 
starting  point  of  the,  443f 
subject-matter  of,  If 
thought  and   the,   2f 
Series,  causal,  448f 

continuous,  203 

Sidgwick,  an  analogical  reasoning,  566 
on  petit io  principii,  570 
on     subject    and    predicate 

terms,  87 

Sorites,  Aristotelian,  332 
defined,    332 
Goclenian,  332f 
rules    of,    335f 

Statistical    Methods,    as    methods    of 
observation,    393 


600 


INDEX 


empirical        generalisation 

and,   391f 

induction   and,    391f 
logical  character  of,  389f 
quantitative,  392f 
Subalternation,    fallacies   of,   528f 
meaning  of,   269f 
Subcontrariety,   fallacies  of,  526f 
meaning  of,  273f 
Syllogism,  as  method,  209,  305 
categorical,  297f,  326f 
categorical,  Figures  of,  310f 
categorical,  Moods  of,  315f 
disjunctive,    343f 
disjunctive,  Moods  of,  344f 
disjunctive,  validity  of,  345f 
hypothetical,  348f,  539f 
hypothetical,  Moods  of,  350f 
judgment  and,  298f 
major   term  and,  304 
mathematical         proportion 

and,  300f 

minor  term  and,  304 
mixed  disjunctive,   343f 
nature  of,  301f,  326,  538f 
problem    of,    298f 
propositions  and,   304 
place  of  conclusion  in,  301f 
quality    of   propositions   in, 

307f 
quantity  of  propositions  in, 

308f 

relation   of   Moods   to   Fig- 
ure  in,   318f 

relation  of  premises  to,  302 
rule  of  disjunctive,  344 
rules  of   categorical,   305f 
rules    of    Figures    in    cate- 
gorical,  312f 
simple   disjunctive,    343f 
structural     view     of     cate- 
gorical,  303f 

two  ways  of  regarding,  326f 
valid    Moods    of    categori- 
cal, 816f,  34« 


Tautology,  logical  status  of,  238,  240 
Terms,  absolute,  141 

abstract,   130f 

classification   of,   169 

collective,    128f 

common,   125f 

complementary,    211 

concrete,   118,   119f 

connotative  use  of,  109f 

contradictory,  529f 

contradictory   opposite,    210 

contrary,   155,  529 

correlative,   143 

definition   of,    159 

denotative  use  of,  108f,  114f 

designations  as,  122f 

disparate,    155 

distribution  of,  114f,  116 

extent  of,  115 

fallacies   of,  534f 

general,  125f,  213 

indefinite,  151 

indesignate,  151 

indeterminate,   211 

individual,   120f,    126,   141 

individual  collective,  129 

infinite,    151 

many  worded,    91 

names    and,    88f 

negative,    I51f,    154,    237f 

positive,  144 

predicate,   85,   86f,   237 

privative,    153f 

problems  of  the  connotative 
and  denotative  use  of,  117, 
158 

proper  names  as,   121f 

propositions  and,  85,  107,  234 

relation  of  connotative  and 
denotative  use  of,  HOf 

relation  of  individual  to  gen- 
eral collective,  130 

relative,   141f 

sign   of  distributed,   115 

sign  of  undistributed,  116 


INDEX 


601 


single-worded,  91 
singular,   I20f,   126 
subject,   85,   86f 
syllogism   and,  304 
thing  and   concrete,   118f 
width  of,  115 
Theatre,   idols   of,   569f 
Theory,   hypothesis  and,  429f 
Thing,  concrete  term  and,  118f 
meaning    of,    119 
predication  and  kinds  of,  160, 

181f 
Thorndike,  on  statistics  of  individuals, 

390f 
Thought,  as  assertion,  28 

comparison  and,  303 
conditions   of   systematic,   7f 
content  and,  29 
immediate,   303 
judgment  and,  28f 
knowledge  and,  2f 
logical  meaning  of,  26f,  28 
logic   and,    lOf 
mediate,  303 
method  of,  logic  as,  29 
nature  of,  2f,  28 
practical  aspect  of,  35f 
syllogistic,   304 
theoretical  aspect  of,   35f 
uses  of  the  term,  26f 
Translation,   ambiguity   and,   165f 

when   employed,  166f 
Truth,    assertion    and,    58 
fact  and,  366f 

grounds  of,  in  induction,  387f 
hypothesis  and,  427 
nature  of,  58f 
systematic,  367 
syllogism   and,  327 


tests   of,    59,    60f 
the  proposition  and,  76f 
Tyndall,    on    the    proof    of    an    induc- 
tion, 427 

on  the  scientific  imagination, 
422,    424,    426 

u 

Unconditional,  meaning  of,  459f 

necessity  and,  456f 
Undistributed,   meaning   of,  115 
Universals,    problem    of,    92 
Universe  of  Discourse,  indeterminate- 
ness  of,  53f 
nature  of,  52f 
plurality  of,  57f 
relation  of  judgment  and 
proposition  to,  54,  82,  87 
vvrepov  Trporepov,  fallacy  of,  572 


Verification,   of  hypothesis,  427f 

the  test  of  truth,  59,  60f 

w 

Welton,  on  ignoratio  elenchi,  574 

on  experimentation,  403 
Whateley,  on  ignoratio  elenchi,  574 
on  petitio  principii,  572 
Whewell,  his  contribution  to  inductive 

logic,  472 

on  colligation,  378f 
on    practical    inferences,    397 
Words,   categorematic,   90 

indefiniteness    in   meaning   of, 

161f 

logical  classification  of,  90 
significant,  as  terms,  89,  160 
syncategorematic,  90 


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